You bought one of Great White Shark Repellant Co.’s 9 percent coupon bonds one y

Question

You bought one of Great White Shark Repellant Co.’s 9 percent coupon bonds one year ago for $810. These bonds make annual payments and mature 8 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 11 percent. If the inflation rate was 3.4 percent over the past year, what was your total real return on investment?

rev: 09_20_2012

26.00%

17.95%

18.75%

7.11%

17.85%

You bought one of Great White Shark Repellant Co.’s 9 percent coupon bonds one year ago for $810. These bonds make annual payments and mature 8 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 11 percent. If the inflation rate was 3.4 percent over the past year, what was your total real return on investment?

Explanation / Answer

First you must calculate what you could sell the bond for today.    

Price (Present Value)= coupon(1.11^-1) + coupon(1.11^-2) +...+coupon(1.11^-8) + par(1.11^-8)

assuming par = $1000, calculate the PV of par..

.use a financial calculator, or...

1000(1.11^-8) = 433.93

using PV of an ordinary annuity formula, calc the PV of the coupons..
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]

your coupon pmt. is $1000 * 0.09 = $90

PVoa = 90 [(1 - (1 / (1.11^8)) / 0.11]

=90*(1-1/(1.11^8))/0.11

463.151

add PV of par + PV of coupons = Price
433.93 + 463.151 = 897.081

cash flows: Sale price - purchase price + one coupon

897.081- 810 + 90 = 177.08

Return before accounting for inflation = net proceeds/initial investment = 177.08 / 810 = 21.86%

the formula for Nominal rate..(1 + Nominal) = (1+Real rate)(1+inflation rate)
solving for real return...
1.2186 = (1 + Real)(1.034)

Real rate = 17.85%

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