Session 6 July 22, 2014 Final Review 1 Introduction to CPCU 540 Financial Calculations and using the Financial Calculator Order of Operations PPMDAS (Pretty Please My Dear Aunt Sally) Parenthesis ( ) Powers ^ or 1n Multiplication x Division or / Addition + Subtraction Reminder: Roots are powers (example square root = ^ ), but also treated as parenthesis (operations must be done inside before applying the root). Example: ( 2 + 4 ) 2 x 2 25 16 62x29 36 x 2 3 72 3 = = = = 24
Yes: 25 16 = 9 = 3 No: 25 16 = 25 - 16 = 5 4 = 1 2 Introduction to CPCU 540 Financial Calculations and using the Financial Calculator Texas Instruments BA-II Plus Financial Calculator Important Buttons Standard Keys Number keys and decimal point ( ) xy x + = and + I (positive/negative) Note: remember the difference between ENTER and Equals (=) Important Time Value of Money (TVM) Keys N = Number of Years I/Y = Interest Rate per Year PV = Present Value PMT = PMT per Period FV = Future Value 2ND = Do the function in Yellow above key P/Y = Number of Payments per Year BGN = Beginning (for annuity due) CF = Cash Flow NPV = Net Present Value IRR = Internal Rate of Return RESET = for resetting calculator in between calculations to clear entries 3 Introduction to CPCU 540 Financial Calculations and using the Financial Calculator HP 10bII Financial Calculator
Important Buttons Standard Keys Number keys and decimal point ( ) xy x + = and + I (positive/negative) Important Time Value of Money (TVM) Keys N = Number of Years I/YR = Interest Rate per Year PV = Present Value PMT = PMT per Period FV = Future Value Orange = Do the function in Orange below key P/YR = Number of Payments per Year END = Payment at End of Year (Ordinary Annuity) BGN = Payment at Beginning of Year (Annuity Due) CF = Cash Flow NPV = Net Present Value EFF % = Effective Rate of Return C ALL = for resetting calculator in between calculations to clear entries 4 Chapter 2 GAAP Financial Statements Types of Financial Statements Income Statement shows an organizations profit or loss over a stated period. Revenue Cost of Goods Sold Revenue sales of products and services Expenses Operating related to sales (commissions) or general operating expenses (rent). Cost of goods sold recognizes the cost of purchasing inventory. Cost of Goods Sold = Beginning Inventory + Additions to Inventory Ending Inventory Gross Profit expresses the amount earned on sales and the costs of those goods only. Gross Profit = Sales Cost of Goods Sold
Gross Margin profit as a percentage of gross sales. Gross Margin = Gross Profit Sales Operating Income results after operating expenses are deducted from gross profit. Operating Income = Gross Profit Operating Expenses Net Income the profit or loss after all factors have been deducted Net Income = Revenue Expenses (including depreciation) + Gains Losses Taxes 5 Chapter 5 Insurer Statutory Annual Statement Analysis Written Premium the amount of premium written for a policy period. Earned Premium the portion of written premium that has been earned based on the amount of coverage provided for the time that has passed. Earned Premium = Written Premium x Example: A six month auto policy is written from April 1 October 1 for $350. How much is earned after two months? # of days into policy period # of days in policy period Earned Premium = $350 x ( 61 days 183 days ) = $350 x .3333 = $116.67 Unearned Premium the amount of premium for a policy period that has not been earned (the remainder after Earned Premium has been subtracted from Written Premium. Unearned Premium = Written Premium x Example: A six month auto policy is written from April 1 October 1 for $350. How much is unearned
after five months? # of days left in policy period # of days in policy period Unearned Premium = $350 x ( 30 days 183 days ) = $350 x .1639 = $57.38 6 Chapter 5 Insurer Statutory Annual Statement Analysis Loss Ratio, Expense Ratio, & Combined Ratio Loss Ratio = ( Incurred Loss + LAE ) Earned Premiums Incurred Losses include Paid Losses and Outstanding Losses Earned Premiums are used because Losses are only paid if coverage is provided, meaning that the premium has been earned. Used to express what percentage of premium went toward losses. Example: What is the companys Loss Ratio with the following amounts? Paid Losses = $3,000,000 Outstanding Losses = $1,000,000 Loss Adjustment Expense = $300,000 Earned Premium = $7,000,000 Loss Ratio = (Incurred Loss + LAE) Earned Premium = (Paid Loss + Outstanding Loss + LAE) Earned Premium = ($3,000,000 + $1,000,000 + $300,000) $7,000,000 = $4,300,000 $7,000,000 = 0.6143 or 61.43%
Expense Ratio = Underwriting Expenses Written Premiums Underwriting expenses include all costs of underwriting the business Written Premium is used because this measures the cost of underwriting the business, before any premium has been earned. Used to express what percentage of business went towards underwriting. Example: What is the companys Expense Ratio with the following amounts? Expense Ratio = Underwriting Expenses Written Premium = $3,300,000 $8,000,000 Underwriting Expenses = $3,300,000 = 0.4125 or 41.25% Written Premium = $8,000,000 7 Chapter 5 Insurer Statutory Annual Statement Analysis Loss Ratio, Expense Ratio, & Combined Ratio Combined Ratio = Expense Ratio + Loss Ratio Combines the two formulas to determine if the company made an underwriting profit by combining underwriting expense and losses. Anything below 100% indicates an underwriting profit. Example: What is the companys Combined Ratio based on the previous slides? Expense Ratio = 41.25%
Loss Ratio = 61.43% Combined Ratio = Expense Ratio + Loss Ratio = 41.25% + 61.43% = 102.68% Operating Ratio = Combined Ratio Investment Income Ratio Measures overall pre-tax profit from underwriting activities and investments. Because positive investment return improves the overall results it is subtracted from the Combined Ratio. Example: What is the companys Operating Ratio with the following amounts? Combined Ratio = 102.68% Investment Income = $285,500 Earned Premium = $7,000,000 Operating Ratio = Combined Ratio Investment Income Ratio = Combined Ratio (Investment Income Earned Premium) = 1.0268 ($285,500 $7,000,000) = 102.68% 4.08% = 98.60% 8 Chapter 5 Insurer Statutory Annual Statement Analysis Key Financial Concepts Capacity Capacity: the amount of capital available to underwrite loss exposures. Greater Written Premium means that greater Policyholders Surplus to provide a cushion against adverse operating results. This is especially true for new business or new lines of business, which tends to have a higher loss ratio due to unfamiliarity with the business. Because the expense to acquire business is recognized at inception, but premiums is only earned, or
recognized, over the policy period, writing additional business reduces Policyholders Surplus. Capacity Formulas Premium-to-Surplus (Leverage) Ratio net written premium divided by surplus. Higher ratio indicates greater leverage (aggressive) and lower capacity to write new business. 3:1 considered problematic by the NAIC and state regulators, but this can vary by the line of business written. Can be impacted by underwriting results, growth of written premium, reinsurance programs, and investment results. Premium-to-Surplus Ratio = Net Written Premium Policyholders Surplus = (Written Premium Ceding Commission Reinsurance Premium) Policyholders Surplus Reserves-to-Surplus Ratio relates to the amount of reserves supported by each dollar of surplus. Underestimation of Loss and LAE reserves can have a significant impact, especially if the ratio is high. No benchmark has been established. Reserves-to-Surplus Ratio = Outstanding Loss & LAE Reserves Policyholders Surplus 9 Chapter 5 Insurer Statutory Annual Statement Analysis Key Financial Concepts Liquidity Liquidity: ability to raise cash and meet financial obligations. Depends on cash inflows/outflows, the relationship between assets and liabilities, and the type and amount of assets available to meet obligations. Measured from underwriting and investment inflows of premiums and investments and outflows of claim payments, investment purchases, and dividends. Also measured by comparing highly liquid assets to current obligations including unearned premium and loss reserves. If an insurer must sell illiquid asset to meet obligation its position is unsatisfactory. Liquidity Formula Liquidity Ratio compares liquid assets to unearned premium and Loss & LAE reserves to measure to what degree an insurer is able to convert assets to cash to settle current obligations. A ratio of 1.0 or greater is desired. No benchmark has been defined beyond this. Liquidity = (Cash + Marketable Securities) (Unearned Premium Reserve + Loss & LAE Reserve) 10 Chapter 6 Cash Flow Valuation
Future and Present Value Calculations by Hand Future Value = how much a given amount of money today will be worth in the future. Annual Compounding FV = PV x ( 1 + r ) n Multiple Compounding FV = PV x ( 1 + r m) n x m FV = Future Value PV = Present Value r = Interest Rate n = Number of Years FV = Future Value PV = Present Value r = Interest Rate n = Number of Years m = number of times per year interest is paid. Using Table FV = PVn x FVfactor Present Value = how much a given amount of money in the future is worth today. FV = PV x ( 1 + r ) n FV ( 1 + r ) n = PV PV = FV ( 1 + r ) n Annual Compounding PV = FV ( 1 + r ) n Multiple Compounding PV = FV ( 1 + r m) n x m Using Table
PV = FVn x PVfactor 11 Chapter 6 Cash Flow Valuation Future Value Calculations Future Value = how much a given amount of money today will be worth in the future. Example If I give you $1,000 today and you put that money into an account earning 6%, how much is it worth in one year, assuming annual compounding? PV = 1,000 r = .06 n=1 FV = ? What if invested for five years? PV = 1,000 x (1 + .06) 5 Example If I give you $1,000 today and you put that money into an account earning 6%, how much is it worth in five years, assuming daily compounding? PV = 1,000 r = .06
n=5 m = 365 FV = ? FV = PV x (1 + r) n FV = 1,000 x (1 + 0.06) 1 FV = 1,000 x (1.06) 1 FV = 100 x 1.06 FV = 1,060 PV = 1,338.23 FV = PV x (1 + r m) n x m FV = 1,000 x (1 + 0.06 365) 5 x 365 FV = 1,000 x (1 + 0.00016438) 1,825 FV = 1,000 x (1.00016438) 1,825 FV = 1,000 x 1.3498 FV = 1,349.83 12 Chapter 6 Cash Flow Valuation FV (Annual Compounding) using TI BAII Plus Example If I give you $1,000 today and you put that money into an account earning 6%, how much is it worth in one year assuming annual compounding? PV = -1,000 I/Y = 6% N=1 P/Y = 1 CPT = FV
Step 1: Reset the calculator 2nd, +/- (Reset), Enter, 2nd, CPT (Quit) Step 2: Set P/Y to 1 2nd, I/Y (P/Y), 1, Enter, 2nd, CPT (Quit) Step 3: Enter your TVM Variables 1,000, +/-, PV 6, I/Y FV = 1,060.00 1, N CPT, FV 13 Chapter 6 Cash Flow Valuation FV (Annual Compounding) using the HP 10bII Example If I give you $1,000 today and you put that money into an account earning 6%, how much is it worth in one year assuming annual compounding? PV = -1,000 I/YR = 6% N=1 P/YR = 1 CPT = FV Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 1 1, Orange, PMT (P/YR), C Step 3: Enter your TVM Variables 1,000, +/- , PV 6, I/YR
1, N FV = 1,060.00 FV 14 Chapter 6 Cash Flow Valuation Present Value Calculations Present Value = how much a given amount of money in the future is worth today. Example If I gave you $1,000 in one year how much is it worth today, assuming 6% interest per year with annual compounding? FV = 1,000 r = .06 n=1 PV = ? What if it is given to you in five years? PV = 1,000 (1 + .06) 5 Example If I give you $1,000 in five years how much is it worth today, assuming 6% interest per year with daily compounding? FV = 1,000 r = .06
n=5 m = 365 PV = ? PV = FV (1 + r) n PV = 1,000 (1 + .06) 1 PV = 1,000 (1.06) 1 PV = 1,000 1.06 PV = 943.40 PV = 747.26 PV = FV (1 + r m) n x m PV = 1,000 (1 + .06 365) 5 x 365 PV = 1,000 (1 + 0.00016438) 1,825 PV = 1,000 (1.00016438) 1,825 PV = 1,000 1.3498 PV = 740.84 15 Chapter 6 Cash Flow Valuation PV (Monthly Compounding) using the TI BAII Plus Example If I give you $1,000 five years from now, how much is it worth today, assuming 6% interest per year with daily compounding? FV = 1,000 I/Y = 6% N=5 P/Y = 365 PV = ? Step 1: Reset the calculator
2nd, +/- (Reset), Enter, 2nd, CPT (Quit) Step 2: Set P/Y to 365 2nd, I/Y (P/Y), 365, Enter, 2nd, CPT (Quit) Step 3: Enter your TVM Variables 1,000, FV 6, I/Y PV = -740.84 nd 5, 2 , N (xP/Y), N CPT, PV 16 Chapter 6 Cash Flow Valuation PV (Monthly Compounding) using the HP 10bII Example If I give you $1,000 five years from now, how much is it worth today, assuming 6% interest per year and daily compounding? FV = 1,000 I/YR = 6% N=5 P/YR = 365 PV = ? Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 365 365, Orange, PMT (P/YR), C Step 3: Enter your TVM Variables 1,000, FV 6, I/YR 5, Orange, N (xP/YR), N
PV PV = -740.84 17 Chapter 6 Cash Flow Valuation Effective Annual Interest Rate Effective Annual Interest Rate: interest is stated at its annual rate, but if the interest is compounded more frequently the effective interest rate is higher than the stated rate. Example: What is the Future Value of $300 at the end of one year with a 4% interest rate compounding annually? Semi-annually? Quarterly? Monthly? Weekly? Annually Semi-Annual Quarterly Monthly Weekly FV = 300 x (1 + .04 1) 1 x 1 FV = 300 x (1 + .04 2) 1 x 2 FV = 300 x (1 + .04 4) 1 x 4 FV = 300 x (1 + .04 12) 1 x 12 FV = 300 x (1 + .04 52) 1 x 52 EAR = (1 + .04 1) 1 x 1 EAR = (1 + .04 2) 1 x 2 EAR = (1 + .04 4) 1 x 4 EAR = (1 + .04 12) 1 x 12 EAR = (1 + .04 52) 1 x 52 = = = = =
1.04000 1.04040 1.04060 1.04074 1.04079 = = = = = = = = = = 312.00 312.12 312.18 312.22 312.24 (1.04000 1) x 100 (1.04040 1) x 100 (1.04060 1) x 100 (1.04074 1) x 100 (1.04079 1) x 100 = = = = =
4.000% 4.040% 4.060% 4.074% 4.079% 18 Chapter 6 Cash Flow Valuation Future Value of an Ordinary Annuity Future Value of an Ordinary Annuity = how much a given series of payments paid at the end of the year will be worth in the future? FV = PV x (1 + r) 0 + PV x (1 + r) 1 + PV x (1 + r) 2 + + PV x (1 + r) n - 1 Example: What is the Future Value of $300 payments at the end of each year for six years, earning 4% interest per year with annual compounding? First payment (end of year) FV = 300 x (1 + .04) 0 = 300.00 Payment at end of 2nd year FV = 300 x (1 + .04) 1 = 312.00 Payment at end of 3rd year FV = 300 x (1 + .04) 2 = 324.48 Payment at end of 4th year FV = 300 x (1 + .04) 3 = 337.46 Payment at end of 5th year FV = 300 x (1 + .04) 4 = 350.96 Payment at end of 6th year FV = 300 x (1 + .04) 5 = 365.00 = 1,989.90
PMT = 300 Note: Your calculator is automatically set to make payments at the end of the year (END) PMT @ END N=6 I/Y = 4% m=1 FV = 1,989.89 FV = ? Using Table FVA = A x FVAF FVAF is the intersection on the table between the Period in Years n and the Interest Rate r 19 Chapter 6 Cash Flow Valuation Present Value of an Ordinary Annuity Present Value of an Ordinary Annuity = how much a series of payments made at the end of the year are worth today, with a given time period and rate of interest. PV = FV (1 + r) 1 + FV (1 + r) 2 + FV (1 + r) 3 + + FV (1 + r) n Example: What is the Present Value of $300 payments at the end of each year for six years, earning 4% interest per year with annual compounding? First payment (end of year) PV = 300 (1 + .04) 1 = 288.46 Payment at end of 2nd year PV = 300 (1 + .04) 2 = 277.37 Payment at end of 3rd year
PV = 300 (1 + .04) 3 = 266.70 Payment at end of 4th year PV = 300 (1 + .04) 4 = 256.44 Payment at end of 5th year PV = 300 (1 + .04) 5 = 246.58 Payment at end of 6th year PV = 300 (1 + .04) 6 = 237.09 = 1,572.64 PMT = 300 Note: Your calculator is automatically set to make payments at the end of the year (END) PMT @ END N=6 I/Y = 4% m=1 PV = -1,572.64 PV = ? Using Table PVA = A x PVAF PVAF is the intersection on the table between the Period in Years n and the Interest Rate r 20 Chapter 6 Cash Flow Valuation PV of Ordinary Annuity using the TI BAII Plus
Example If you receive $300 payments for six years at 4% interest per year, assuming annual compounding, what is the Present Value of those payments if the payments are made at the end of the year? PMT = 300 PMT @ END I/Y = 4% N=6 P/Y = 1 PV = ? Step 1: Reset the calculator 2nd, +/- (Reset), Enter, 2nd, CPT (Quit) Step 2: Set P/Y to 1 2nd, I/Y (P/Y), 1, Enter, 2nd, CPT (Quit) Step 3: Enter your TVM Variables 300, PMT 4, I/Y PV = -1,572.64 nd 6, 2 , N (xP/Y), N CPT, PV 21 Chapter 6 Cash Flow Valuation PV of Ordinary Annuity using the HP 10bII Example If you receive $300 payments for six years at 4% interest per year, assuming annual compounding, what is
the Present Value of those payments if the payments are made at the end of the year? PMT = 300 PMT @ END I/YR = 4% N=6 P/YR = 1 PV = ? Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 1 1, Orange, PMT (P/YR), C Step 3: Enter your TVM Variables 300, PMT PV = -1,572.64 4, I/YR 6, N PV 22 Chapter 6 Cash Flow Valuation Future Value of an Annuities Due Future Value of an Annuity Due = how much a given series of payments will be worth in the future if payments are made at the beginning of the year. Note: because the first payment is made immediately it can earn interest over the year. FV = PV x (1 + r) 1 + PV x (1 + r) 2 + PV x (1 + r) 3 + + PV x (1 + r) n Example: What is the Future Value of $300 payments at the beginning of each year for six years, earning 4% interest per year with annual compounding? Payment at beginning of 1st year Payment at beginning of 2nd year
Payment at beginning of 3rd year Payment at beginning of 4th year Payment at beginning of 5th year Payment at beginning of 6th year FV = 300 x (1 + .04) 1 FV = 300 x (1 + .04) 2 FV = 300 x (1 + .04) 3 FV = 300 x (1 + .04) 4 FV = 300 x (1 + .04) 5 FV = 300 x (1 + .04) 6 PMT = 300 PMT @ BGN N=6 I/Y = 4% m=1 FV = ? = 312.00 = 324.48 = 337.46 = 350.96 = 365.00 = 379.60 = 2,069.50 FV = 2,069.49 23 Chapter 6 Cash Flow Valuation Present Value of an Annuity Due Present Value of an Annuity Due = how much a given payment made at the beginning of the year in the future will be worth today.
PV = FV (1 + r) 0 + FV (1 + r) 1 + FV (1 + r) 2 + + FV (1 + r) n - 1 Example: What is the Present Value of $300 payments at the beginning of each year for six years, earning 4% interest per year with annual compounding? Payment at beginning of 1st year Payment at beginning of 2nd year Payment at beginning of 3rd year Payment at beginning of 4th year Payment at beginning of 5th year Payment at beginning of 6th year PV = 300 (1 + .04) 0 PV = 300 (1 + .04) 1 PV = 300 (1 + .04) 2 PV = 300 (1 + .04) 3 PV = 300 (1 + .04) 4 PV = 300 (1 + .04) 5 PMT = 300 PMT @ BGN N=6 I/Y = 4% m=1 PV = ? = 300.00 = 288.46 = 277.37 = 266.70 = 256.44 = 246.58 = 1,635.55 PV = -1,635.55 24
Chapter 6 Cash Flow Valuation FV of Annuity Due using the TI BAII Plus Example If you receive $300 payments for six years at 4% interest per year, assuming annual compounding, what is the Future Value of those payments if the payments are made at the beginning of the year? PMT = 300 PMT @ BGN I/Y = 4% N=6 P/Y = 1 FV = ? Step 1: Reset the calculator 2nd, +/- (Reset), Enter, 2nd, CPT (Quit) Step 2: Set P/Y to 1 2nd, I/Y (P/Y), 1, Enter, 2nd, CPT (Quit) Step 3: Set PMT to BGN 2nd, PMT (BGN), 2nd, Enter, 2nd, CPT (Quit) Step 4: Enter your TVM Variables 300, PMT 4, I/Y FV = 2,069.49 nd 6, 2 , N (xP/Y), N CPT, FV 25 Chapter 6 Cash Flow Valuation
FV of Annuity Due using the HP 10bII Example If you receive $300 payments for six years at 4% interest per year, assuming annual compounding, what is the Future Value of those payments if the payments are made at the beginning of the year? Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 1 1, Orange, PMT (P/YR), C PMT = 300 PMT @ BGN I/YR = 4% N=6 P/YR = 1 FV = ? Step 3: Set PMT to BGN Orange, MAR Step 3: Enter your TVM Variables 300, PMT FV = 2,069.49 4, I/YR 6, N FV 26 Chapter 6 Cash Flow Valuation Perpetuities
Perpetuity: a series of fixed payments made on specific dates over an indefinite period. Where annuities have a set period of time over which payments are made, perpetuities make payments indefinitely. To compare this alternative investments of a similar risk you need to compare Present Values of each investment. Perpetuity Formula PVP = A r PVP = Present Value of Perpetuity A = Payment per Period r = discount rate (interest rate on alternative investment) Example: If a perpetuity provides an annual payment of $30,000 and 6% interest could be earned on an alternative investment with a similar risk profile, what is the Present Value of the perpetuity? A = 30,000 R = 6%, or 0.06 PVP = ? PVP = A r PVP = 30,000 0.06 PVP = 500,000 27 Chapter 6 Cash Flow Valuation Net Present Value NPV: the difference between the present value of cash inflows and outflows. Organizations generally use NPV to determine if an investment is worth making and to compare between multiple investments. Generally, investments are only made if the NPV is greater than zero. Required rate of return should at least equal cost of capital. NPV = C0 + ( Ct ( 1 + r ) t ) + + ( Cn ( 1 + r ) n )
C0 = Cash outflow at the beginning of the project Ct = Payment (inflow) at period t for t = 1 through t = n r = discount rate n = number of periods Example: A business is looking to invest $30,000 in a new IT system. It will take four years bring each line of business online, but they expect savings of $5,000 the first year, $7,500 the second year, $10,000 the third year, and $12,000 the fourth year. At a required rate of return of 6%, is it worth it? NPV = C0 + ( Ct ( 1 + r ) t ) + + ( Cn ( 1 + r ) n ) NPV = 30,000 + 5,000 (1 + .06)1 + 7,500 (1+.06)2 + 10,000 (1+.06)3 + 12,000 (1+.06)4 NPV = 30,000 + 5,000 1.06 + 7,500 1.1236 + 10,000 1.1910 + 12,000 1.2625 NPV = 30,000 + 4,716.98 + 6,674.97 + 8,396.34 + 9,504.95 NPV = 706.73 NPV < 0 = No 28 Chapter 6 Cash Flow Valuation Net Present Value using the TI BAII Plus CF0 = -30,000 Example: It costs $30,000 to C01 = 5,000 implement, but expect savings of C02 = 7,500 $5,000 the first year, $7,500 the second year, $10,000 the third C03 = 10,000 year, and $12,000 the fourth year. At a required rate of return C04 = 12,000 of 6%, is it worth it? I/Y = 6 CPT = NPV Step 1: Reset the calculator 2nd, +/- (Reset), Enter, 2nd, CPT (Quit)
Step 2: Set P/Y to 1 2nd, I/Y (P/Y), 1, Enter, 2nd, CPT (Quit) Step 3: Enter your Cash Flows CF CF0 = 30000, +/-, Enter, Down Arrow () 5000, Enter, , 7500, Enter, , NPV = -706.73 10000, Enter, , 12000, Enter 29 NPV, 6, Enter, , CPT Chapter 6 Cash Flow Valuation Net Present Value using the HP 10bII Example: It costs $30,000 to implement, but expect savings of $5,000 the first year, $7,500 the second year, $10,000 the third year, and $12,000 the fourth year. At a required rate of return of 6%, is it worth it? CF0 = -30,000 CF1 = 5,000 CF2 = 7,500 CF3 = 10,000 CF4 = 12,000 I/YR = 6 CPT = NPV Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 1
1, Orange, PMT (P/YR), C Step 3: Enter your Cash Flows 30000, Orange, Decimal Point . (+/-), CFj 5000, CFj 7500, CFj NPV = -706.73 10000, CFj 12000, CFj 6, I/YR Orange, PRC (NPV) 30 Chapter 6 Cash Flow Valuation Net Present Value with Repeating Payments In the previous example we looked at a Net Present Value where each payment was unique. What do we do if there are payments that repeat several times? There is an easy way to enter this into your calculator using the same Cash Flow menu we used before, but here we are going to change our F value (TI) or our Nj value (HP). Example: A farmer is looking to invest $100,000 into upgrading a processing building to make his operation more efficient. After being built he expects savings of $12,000 the first five years, and $20,000 the sixth, seventh, and eighth years. At a required rate of return of 3%, is it worth it? NPV = C0 + ( Ct ( 1 + r ) t ) + + ( Cn ( 1 + r ) n ) NPV = 100,000 + 12,000 (1 + .03)1,2,3,4,5 + 20,000 (1 + .03)6,7,8 NPV = 100,000 + 11,650.49 + 11,311.15 + 10,981.70 + 10,661.84 + 10,351.31 + 16,749.69 + 16,261.83 + 15,788.18 NPV = 3,756.19 CF0 = -100,000 C01 = 12,000 NPV > 0 = Yes F01 = 5 NPV = 3,756.19 C02 = 20,000 F02= 3
I/Y = 3 CPT = NPV 31 Chapter 6 Cash Flow Valuation NPV with repeating payments using the TI BAII Plus Example: It costs $100,000 to build, but expect increased efficiency of $12,000 the first five years and $20,000 the sixth, seventh, and eighth years. At a required rate of return of 3%, is it worth it? CF0 = -100,000 C01 = 12,000 F01 = 5 C02 = 20,000 F02 = 3 I/Y = 3 Step 1: Reset the calculator CPT = NPV 2nd, +/- (Reset), Enter, 2nd, CPT (Quit) Step 2: Set P/Y to 1 2nd, I/Y (P/Y), 1, Enter, 2nd, CPT (Quit) Step 3: Enter your Cash Flows CF 100000, +/-, Enter, Down Arrow () 12000, Enter, 5, Enter, NPV = 3,756.19 20000, Enter, 3, Enter
NPV, 3, Enter, , CPT 32 Chapter 6 Cash Flow Valuation NPV with repeating payments using the HP 10bII Example: It costs $100,000 to build, but expect savings of $12,000 the first five years and $20,000 the sixth, seventh, and eighth years. At a required rate of return of 3%, is it worth it? CFJ0 = -100,000 CFJ1 = 12,000 NJ1 = 5 CFJ2 = 20,000 NJ2 = 3 I/YR = 3 CPT = NPV Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 1 1, Orange, PMT (P/YR), C Step 3: Enter your Cash Flows 100000, Orange, Decimal Point . (+/-), CFj 12000, CFj 5, Orange, (CFj ) Nj NPV = 3,756.19 20000, CFj 3, Orange, (CFj ) Nj 3, I/YR Orange, PRC (NPV) 33
Chapter 7 Bonds and Stocks Bond Characteristics Bonds: debt instrument that is purchased at a price and can make payments in future until final maturity, when face value is paid. Maturity Date date at which principal or par value is paid to bondholder. Principal, Face Value, Par Value the amount borrowed, as shown on the front of the bond, and to be paid at maturity. Price of Bond = % of Face Value Example: $100,000 bond with 200 units ($500 per unit) is priced at 85% of face value. Price of Bond = 0.85 x $100,000 = $85,000 or $500 * .85 x 200 units = $85,000. Coupon Rate bonds annual interest rate, stated as a percentage of the par value. Coupon Rate = Annual Coupon Face Value Example: $10,000 face value bond pays an annual coupon of $200. Example: A bond pays a coupon of $200 with a Coupon Rate of 2%. Coupon Rate = 200 10,000 Coupon Rate = 0.02 or 2% 2% = 200 Face Value Face Value = 200 0.02 = $10,000 Example: A $10,000 face value bond pays a 2% coupon. 0.02 = Annual Coupon $10,000 Annual Coupon = 0.02 x 10,000 = 200 Rate of Return for a specified period is the % of Value Earned for that period. Rate of Return = (Coupon Payments + Capital Gain/Loss) Face Value Rate of Return = ( (5 x 200 ) + (10,000 9,100) ) 10,000
Rate of Return = (1000 + 900) 10,000 Rate of Return = 1,900 10,000 Rate of Return = 0.19 or 19% 34 Chapter 7 Bonds and Stocks Bond Pricing Example Example: A $5,000 par value, 10-year bond with three years to maturity, with a 8% coupon, and a market required rate of return of 5%. Coupon Payment = 5,000 x .08 C = 400 n=3 r = .05 FaceValue = 5,000 Bond Price = C1 (1 + r)n + C2 (1 + r)n + C3 (1 + r)n + FaceValue (1 + r)n Bond Price = 400 (1 + .05)1 + 400 (1 + .05)2 + 400 (1 + .05)3 + 5,000 (1 + .05)3 Bond Price = 400 (1.05) + 400 (1.05)2 + 400 (1.05)3 + 5,000 (1.05)3 Bond Price = 400 1.05 + 400 1.1025 + 400 1.1576 + 5,000 1.1576 Bond Price = 380.95 + 362.81 + 345.54 + 4,319.19 Bond Price = 5,408.49 Looks a lot like a PV function of future cash flows or a NPV, but without the C0 Because the bond is priced above its par value it is said to be selling at a premium. 35 Chapter 6 Cash Flow Valuation Bond Pricing using the TI BAII Plus CF0 = 0
C01 = 400 Example: What is the cost of a F01 = 1 $5,000 par value, 10-year C02 = 400 bond with three years to maturity, with a 8% coupon, F02 = 2 and a market required rate of C03 = 5400 return of 5%? F02 = 1 I/Y = 5 Step 1: Reset the calculator CPT = NPV 2nd, +/- (Reset), Enter, 2nd, CPT (Quit) Step 2: Set P/Y to 1 2nd, I/Y (P/Y), 1, Enter, 2nd, CPT (Quit) Step 3: Enter your Cash Flows CF NPV = 5,408.49 Down Arrow () 400, Enter, , Note Because the 1st 400, Enter, , and 2nd Payments are the 5400, Enter, same you could also set F1 = 2, and CF2 = 5400. NPV, 5, Enter, , CPT 36 Chapter 6 Cash Flow Valuation Bond Pricing using the HP 10bII
Example: What is the cost of a $5,000 par value, 10-year bond with three years to maturity, with a 8% coupon, and a market required rate of return of 5%? CFJ0 = 0 CFJ1 = 400 NJ1 = 1 CFJ2 = 400 NJ2 = 1 CFJ3 = 5400 NJ3 = 1 I/YR = 5 CPT = NPV Step 1: Reset the calculator Orange, C (C All), C Step 2: Set P/Y to 1 1, Orange, PMT (P/YR), C Step 3: Enter your Cash Flows 400, CFj NPV = 5,408.49 400, CFj 5400, CFj Note Because the 1st 5, I/YR and 2nd Payments are the Orange, PRC (NPV) same you could also set NJ1 = 2, and CFJ2 = 5400. 37 Chapter 7 Bonds and Stocks
Stock Characteristics Stocks: represent an ownership interest in the issuing company. Unlike bonds, which are debt instruments, stocks represent ownership and so they have lower priority than bonds during liquidation. This represents additional risk, but also the potential for greater returns. Stocks also exist indefinitely, unlike bonds. Annual Rate of Return for Bonds Annual Rate of Return = (Interest + Capital Gain) Bond price at beginning of year Rate of Return = (Coupon Payments + Capital Gain/Loss) Face Value Rate of Return = ( (5 x 200 ) + (10,000 9,100) ) 10,000 Rate of Return = (1000 + 900) 10,000 Rate of Return = 1,900 10,000 Rate of Return = 0.19 or 19% Annual Rate of Return for Stocks Annual Rate of Return = (Dividends + Capital Gain) Share price at beginning of year Rate of Return = (3.50 + (65 50)) 50 Rate of Return = (3.50 + 15) 50 Rate of Return = 18.50 50 Rate of Return = 0.37 or 37% 38 Chapter 8 Insurer Investment Portfolio Management Quantitative Measures of Risk Mean = average of values in data set. Example: 0, 9, 3, 6, 5, 4, 7, 2, 9 Mean = ( 0 + 9 + 3 + 6 + 5 + 4 + 7 + 2 +9 ) 9 Mean = 45 9 Mean = 5.00 Median = the middle number in a data set. Example: 0, 9, 3, 6, 5, 4, 7, 2, 9 Even number of data points
Example: 0, 9, 3, 6, 5, 4, 7, 2, 9, 6 Median = 0, 2, 3, 4, 5, 6, 7, 9, 9 Median = 5 Median = 0, 2, 3, 4, 5, 6, 6, 7, 9, 9 Median = (5 + 6) 2 = 5.5 Mode = the most common number in a data set. Example: 0, 9, 3, 6, 5, 4, 7, 2, 9 More than one mode Example: 0, 9, 3, 6, 5, 4, 7, 2, 9, 6 Mode = 0, 2, 3, 4, 5, 6, 7, 9, 9 Mode = 9 Mode = 0, 2, 3, 4, 5, 6, 6, 7, 9, 9 Mode = 6, 9 39 Chapter 8 Insurer Investment Portfolio Management Quantitative Measures of Risk While expected rate of return is usually the first consideration, other factors help quantify the risk that the actual return will be higher or lower than expected. Example: 0, 9, 3, 6, 5, 4, 7, 2, 9 Mean = ( 0 + 9 + 3 + 6 + 5 + 4 + 7 + 2 +9 ) 9 = 5 Variance difference of investments return from the average. Low variance indicates that the individual values are near the mean and high variance means the opposite. Variance = Sum of Squared Deviations (n 1) (0 5) 2 = -5 2 = 25
(9 5) 2 = 4 2 = 16 (3 5) 2 = -2 2 = 4 (6 5) 2 = 1 2 = 1 (5 5) 2 = 0 2 = 0 (4 5) 2 = -1 2 = 1 (7 5) 2 = 2 2 = 4 (2 5) 2 = -3 2 = 9 (9 5) 2 = 4 2 = 16 Variance = 25+16+4+1+0+1+4+9+16 9-1 Variance = 9.500 Standard Deviation difference of a value from the mean. Low standard deviation indicates data points are close to the average. However, for data sets with large values, the standard deviation will typically be larger as well, which can be misleading. Standard Deviation = Variance Standard = 25+16+4+1+0+1+4+9+16 Deviation 9-1 Standard Deviation = 3.08 40 Chapter 8 Insurer Investment Portfolio Management Quantitative Measures of Risk
Coefficient of Variation used to compare variation between data sets with similar standard deviations but different means. Coefficient of Variation = Standard Deviation Mean Example: If two data sets have the same mean (5), but one set has a STDEV of 1.157 and the other is 9.463 the first sets values are closer to the mean on average. = 1.157 5 = 0.231 = 9.463 5 = 1.893 Value at Risk a threshold value where the probability of loss is greater than the value based on two factors: Probability of a Loss: the likelihood that loss will occur. Time Horizon: the amount of time over which this loss could occur. Example: The 5%, annual VaR of an investment is $700,000. This means there is a 5% chance of losing $700,000 or more in a year. Beta while other measures compare variability against a rate of return, Beta describes variability in the price of an asset to the variability of an average asset, making it a measure against an overall marketplace. Example: A beta of 1.00 indicates volatility is equal to overall marketplace. A beta of 0.50 indicates it is half as volatile as the marketplace. A beta of 2.00 indicates it is twice as volatile as the marketplace. Chapter 8 Insurer Investment Portfolio Management Portfolio Management Concepts Goal of investment portfolio is to provide highest possible return at an acceptable level of risk and by mixing investments you can optimize your return. Investors and managers are assumed to be risk averse, so given the choice between two investments with equal rates of return, they will always choose that with a lower risk. Typically, risk increases as rate of return increases, known a the risk-return trade-off.
Diversification reducing exposure to company-specific risk by adding other investments to the portfolio. Market risk cannot be eliminated with diversification. Expected return of the portfolio is the weighted average returns of individual securities. Company-specific Risk: risk that affects a specific company or small group of companies. Market Risk: risk affecting the whole market, independent of individual company performance. Example: Year 2006 2007 2008 2009 2010 Mean STDEV Husky Racing Company 4% 17% 12% -10% 8% 6% 10% Bulldog Breeding Farms -2% 17% 10% 13% -6% 6% 10%
Combined Portfolio 1% 17% 11% 2% 1% 6% 7% Chapter 8 Insurer Investment Portfolio Management Bond Portfolio Management Fixed maturity date makes bond portfolio management different than equities because the issuer must repay the principal at a given time and coupon payments are fixed. While cash outflows are largely determined by underwriting losses, with property losses being shorttailed and settled quickly while liability losses can have lengthy time to settlement. Because of this investments must be timed to provide adequate funds. Cash Matching matching maturity and amount with the expected loss payment. Example: Company expects to owe $2.9M at the end of the year. To finance this they purchase a $5M ten year zero coupon (no interest) bond at the current market rate of 6% for what price? PV = 5,000,000 (1 + .06) 10 PV = 5,000,000 1.7908 PV = 2,791,973.89 PV = 5,000,000 (1 + .06) 9 PV = 5,000,000 1.6895 PV = 2,959,492.32 Interest Rate Risk the risk that changes in interest rates will reduce the investments value below what is expected or required. Example: Company purchased the bond outlined above, but over the year interest rates increase to 10%. What effect does this have on the bond? Bond devalued and does not provide funds to pay off the loss. As interest rates rise, the value of the bonds go PV = 5,000,000 (1 + .10) 9
down. Purchasing bond that matures at same time with PV = 5,000,000 2.35795 face value matching expected payment avoids this. PV = 2,120,488.09 43 Chapter 8 Insurer Investment Portfolio Management Matching Investment & Liability Duration Bonds pay interest on a predetermined schedule, but losses may not be due immediately. These funds can then be reinvested, but exposes the company to a new risk. Reinvestment Risk risk that rate at which reinvested funds earn is unfavorable. Example: Bond makes annual coupon payments at 6%, but savings account in which coupons are reinvested only earns 4%. Duration used to measure the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments. Zerocoupon bonds duration is equal to time to maturity. The weighted average life helps compare bonds of different maturities and coupons. Bond A: $10,000 zero-coupon bond maturing in 4 years, purchased for $7,628.95 to yield 7%. Bond B: $10,000 bond maturing in 6 years with a 10% coupon at a 10% market required rate. Year (1) 1 2 3 4 5 6 Cash Flow PV @ 10% % of Total Product (2) (3) (3) 10,000 (4) x (1) 1000 909 0.091
0.091 1000 826 0.083 0.165 1000 751 0.075 0.225 1000 683 0.068 0.273 1000 621 0.062 0.310 11000 6,209 0.621 3.726 Duration 4.791 Based on this we can see the Duration of Bond B is longer than that of Bond A 44 Chapter 10 Capital Management Financial Leverage The use of fixed cost funds (debt) to increase returns to shareholders. Financial Leverage Analysis used for comparing earnings per share under various capital
structures to optimize returns. Interest expense can reduce net income, earnings per share (EPS) and return on equity (ROE) can be increased. Can also be viewed as adding equity or debt to current capital as ROE can be increased without adding any additional equity. Example: As Seen on TV Corporation has an all-equity structure of $20M from 500,000 shares of stock ($40 per share) with earnings of $5M. Under this structure EPS is $10 while ROE is 25%. They require an additional $10M in capital which will increase earnings to $7.5M. They could sell 250,000 shares at $40 per share or acquire the debt at 6% interest, or $600,000 per year. Which would maximize EPS and ROE? Income Statement EBIT Interest Expense Net Income Balance Sheet Liabilities Equity Shares Outstanding ROE EPS Current Stock Debt 5,000,000 0
5,000,000 7,500,000 0 7,500,000 7,500,000 600,000 6,900,000 0 20,000,000 0 30,000,000 10,000,000 20,000,000 500,000 750,000 500,000 25.0% 10.00 25.0% 10.00 34.5% 13.80 45
Chapter 10 Capital Management Insurer Leverage Insurer Cash Flow Funds to generate investment income is provided by policyholders surplus and funds from operations. When premium is received, expenses are paid immediately, but losses arent typically paid until some time later. An insurer may write a policy expecting an underwriting loss (Premium Expenses Losses) because they can earn an adequate rate of return on the funds generated. Insurance Leverage Cash flows provides funds for investments outside of financing and is measured by the ratio of Reserves, which includes Unearned Premium Reserves and Loss & LAE reserves to Written Premium times Insurance Exposure. Insurance Leverage = Insurance Exposure x (Reserves Written Premium) or Reserves = Written Premium x Reserves Policyholders Surplus Policyholders Surplus Written Premium Example: Insurance Leverage = 5,000,000 x 10,000,000 7,500,000 5,000,000 Insurance Leverage = 2,000,000 x 3,000,000 1,000,000 2,000,000 Insurance Leverage = 0.67 x 2 = 1.33 Insurance Leverage = 2.00 x 1.5 = 3.00
46 Chapter 10 Capital Management Cost of Capital from Insurance Operations To determine the cost of obtaining funds from insurance operations due to the timing of cash flows (premium in with expense out, then losses out) we can calculate the discount rate equating the present value of loss payments with the cash inflow from premium less underwriting expense. Another method is to estimate the cost is the ratio of underwriting results to reserves on an after-tax basis. K10 = (1 T) x U (LR + PR) K10 = cost of capital T = tax rate U = underwriting loss LR = Loss & LAE Reserves PR = Unearned Premium Reserves An underwriting loss produces an estimated cost of funds by showing the relationship between the loss and funds generated for investment. If there is an underwriting gain, the formula produces a negative cost policy provides funds for both investment and underwriting profit, which can also be invested. 47 Chapter 10 Capital Management Insurer Cost of Capital Cost of Equity rate of return required by shareholders for use of capital. Two methods for estimating the cost of equity: Discounted Cash Flow (DCF) Model: values an asset as the present value of all future cash flows from that asset in perpetuity. KE = [ (d P) x (1 + g) ] + g
KE = cost of equity d = last dividend paid P = current share price g = expected annual growth rate of the dividend in perpetuity Example: Mid-Mo Mavericks paid a $1.50 dividend last year with a 6% growth rate and a current share price of $100. What is their cost of equity? KE = [ (d P) x (1 + g) ] + g KE = [ (1.50 100) x (1 + .06) ] + .06 KE = [ .02 x 1.06 ] + .06 KE = 0.016 + .06 KE = 0.076 or 7.60% 48 Chapter 10 Capital Management Insurer Cost of Capital Cost of Equity rate of return required by shareholders for use of capital. Two methods for estimating the cost of equity: Capital Asset Pricing Model (CAPM): pricing a security based on the relationship between risk and return. Estimates cost by separating and valuing the two components of risk, unsystematic and systemic risk. KE = cost of equity KE = rf + (rm rf) = Beta of portfolio Rf = Risk-free rate of return Rm = Expected return on the market Example: Mid-Mo Mavericks Beta is 1.5 while the risk-free rate is 3.00% and the expected market return is 7.00%. What is their cost of equity? KE = rf + (rm rf)
KE = 0.03 + 1.50 (0.07 0.03) KE = 0.03 + 1.50 (0.04) KE = 0.03 + 0.06 KE = 0.09 or 9.00% 49 Chapter 10 Capital Management Insurer Cost of Capital Cost of Preferred Stock while stock is equity capital, the cost of preferred stock is calculated like the cost of a bond based on the preferred dividends that are paid. KPS = D PP KPS = cost of preferred stock capital D = dividend paid per share PP = Market price of one share Example: Columbia Insurers Beta preferred share is $125 per share and pays a $5.00 dividend. What is their cost of preferred stock? KPS = D PP KE = 5.00 125 KE = 0.04 or 4.0% 50 Chapter 10 Capital Management Insurer Cost of Capital Cost of Debt rate of return required to compensate a companys debt holders for the use of their capital. The cost of debt is the interest expense, which can be separated into two components: the risk-free rate of return and the risk premium on an after-tax basis.
KD = (rf + risk premium) x (1 t) KD = cost of debt rf = risk-free rate of return t = tax rate Example: The rate of return on U.S. Treasury bills is 3.0% while the risk premium for Mid-Mo Mavericks bonds is 6.0%. At a 35% tax rate, what is their cost of debt? KD = (rf + risk premium) x (1 t) KD = (0.03 + 0.06) x (1 0.35) KD = 0.09 x 0.65 KD = 0.0585 or 5.85% 51 Chapter 10 Capital Management Insurer Cost of Capital Weighted Average Cost of Capital the average cost of equity and debt as a proportion of invested capital. WACC = (Cost of equity x Percentage equity) + (Cost of debt x Percentage debt) Cost of Equity must be broken down into both Common and Preferred Stock WACC = (Cost of Common Stock x % Common Stock) + (Cost of Preferred Stock x % Preferred Stock) + (Cost of debt x % Debt) Example: Based on the Cost of Common Stock, Preferred Stock, and Debt that we calculated for Mid-Mo Mavericks what is their WACC if they represent 45%, 3%, and 52% of their portfolio? Cost of Common Stock = 9.00% Cost of Preferred Stock = 4.00% Cost of Debt = 5.85% WACC = (Cost of equity x Percentage equity) + (Cost of debt x Percentage debt) WACC = (0.09 x 0.45) + (0.04 x 0.03) + (.0585 x 0.52)
WACC = 0.0405 + 0.0012 + 0.0304 WACC = 0.0721 or 7.21% 52 Chapter 11 Mergers & Acquisitions Acquisition Gains and Costs Companies are worth more together if additional net cash inflows result from the combination of the two companies. Only make sense when G > 0. G = VAB (VA + VB) G = Economic Gain VAB = Value of combined companies VA = Value of Company A alone VB = Value of Company B alone Example: Company A is valued at $50M alone while Company B is valued at $200M alone. Their combined value is $300M. Does this acquisition make sense? G = VAB (VA + VB) G = 300 (50 + 200) G = 300 250 G = 50 53
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