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Unformatted text preview: 932.26 – 918.00) / $918.00 = 0.0155 or 1.55% All else held constant, premium bonds pay a high current income while having price depreciation as maturity nears; discount bonds pay a lower current income but have price appreciation as maturity nears. For either bond, the total return is still 7%, but this return is distributed differently between current income and capital gains. 225 24. a. The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM. The bond price equation for this bond is: P0 = $1,140 = $90(PVIFAR%,10) + $1,000(PVIF R%,10) Using a spreadsheet, financial calculator, or trial and error we find: R = YTM = 7.01% b. To find our HPY, we need to find the price of the bond in two years. The price of the bond in two years, at the new interest rate, will be: P2 = $90(PVIFA6.01%,8) + $1,000(PVIF6.01%,8) = $1,185.87 To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond with the cash flows we received. The cash flows we received were $90 each year for two years, and the price of the bond when we sold it. The equation to find our HPY is: P0 = $1,140 = $90(PVIFAR%,2) + $1,185.87(PVIFR%,2) Solving for R, we get: R = HPY = 9.81% The realized HPY is greater than the expected YTM when the bond was bought because interest rates dropped by 1 percent; bond prices rise when yields fall. 25. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is: PM = $800(PVIFA4%,16)(PVIF4%,12) + $1,000(PVIFA4%,12)(PVIF4%,28) + $20,000(PVIF4%,40) PM = $13,117.88 Notice that for the coupon payments of $800, we found the PVA for the coupon payments, and then discounted the lump sum back to today. Bond N is a zero coupon bond with a $20,000 par value; therefore, the price of the bond is the PV of the par, or: PN = $20,000(PVIF4%,40) = $4,165.78 26. To find the present value, we need to find the real weekly interest rate. To find the real return, we need to use the effective annual rates in the Fisher equation. So, we find the real EAR is: (1 + R) = (1 + r)(1 + h) 1 + .107 = (1 + r)(1 + .035) r = .0696 or 6.96% 226 Now, to find the weekly interest rate, we need to find the APR. Using the equation for discrete compounding: EAR = [1 + (APR / m)]m – 1 We can solve for the APR. Doing so, we get: APR = m[(1 + EAR)1/m – 1] APR = 52[(1 + .0696)1/52 – 1] APR = .0673 or 6.73% So, the weekly interest rate is: Weekly rate = APR / 52 Weekly rate = .0673 / 52 Weekly rate = .0013 or 0.13% Now we can find the present value of the cost of the roses. The real cash flows are an ordinary annuity, discounted at the real interest rate. So, the present value of the cost of the roses is: PVA = C({1 – [1/(1 + r)]t } / r) PVA = $8({1 – [1/(1 + .0013)]30(52)} / .0013) PVA = $5,359.64 27. To answer this question, we need to find the monthly interest rate, which is the APR divided by 12. We also must be careful to use the real interest rate. The Fisher equation uses the effective annual rate, so, the real effective annual interest rates, and the monthly interest rates for each account are: Stock account: (1 + R) = (1 + r)(1 + h) 1 + .12 = (1 + r)(1 + .04) r = .0769 or 7.69% APR = m[(1 + EAR)1/m – 1] APR = 12[(1 + .0769)1/12 – 1] APR = .0743 or 7.43% Monthly rate = APR / 12 Monthly rate = .0743 / 12 Monthly rate = .0062 or 0.62% Bond account: (1 + R) = (1 + r)(1 + h) 1 + .07 = (1 + r)(1 + .04) r = .0288 or 2.88% APR = m[(1 + EAR)1/m – 1] APR = 12[(1 + .0288)1/12 – 1] APR = .0285 or 2.85% 227 Monthly rate = APR / 12 Monthly rate = .0285 / 12 Monthly rate = .0024 or 0.24% Now we can find the future value of the retirement account in real terms. The future value of each account will be: Stock account: FVA = C {(1 + r )t – 1] / r} FVA = $800{[(1 + .0062)360 – 1] / .0062]} FVA = $1,063,761.75 Bond account: FVA = C {(1 + r )t – 1] / r} FVA = $400{[(1 + .0024)360 – 1] / .0024]} FVA = $227,089.04 The total future value of the retirement account will be the sum of the two accounts, or: Account value = $1,063,761.75 + 227,089.04 Account value = $1,290,850.79 Now we need to find the monthly interest rate in retirement. We can use the same procedure that we used to find the monthly interest rates for the stock and bond accounts, so: (1 + R) = (1 + r)(1 + h) 1 + .08 = (1 + r)(1 + .04) r = .0385 or 3.85% APR = m[(1 + EAR)1/m – 1] APR = 12[(1 + .0385)1/12 – 1] APR = .0378 or 3.78% Monthly rate = APR / 12 Monthly rate = .0378 / 12 Monthly rate = .0031 or 0.31% Now we can find the real monthly withdrawal in retirement. Using the present value of an annuity equation and solving for the payment, we find: PVA = C({1 – [1/(1 + r)]t } / r ) $1,290,850.79 = C({1 – [1/(1 + .0031)]300 } / .0031) C = $6,657.74 228 This is the real dollar amount of the monthly withdrawals. The nominal monthly withdrawals will increase by the inflation rate each month. To find the nominal dollar amoun...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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