You bought one of Great White Shark Repellant Co.’s 11 percent coupon bonds one

Question

You bought one of Great White Shark Repellant Co.’s 11 percent coupon bonds one year ago for $810. These bonds make annual payments and mature 9 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 13 percent. If the inflation rate was 3.7 percent over the past year, what was your total real return on investment?

You bought one of Great White Shark Repellant Co.’s 11 percent coupon bonds one year ago for $810. These bonds make annual payments and mature 9 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 13 percent. If the inflation rate was 3.7 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(1.13^-1) + coupon(1.13^-2) +...+coupon(1.13^-9) + par(1.13^-9)
assuming par = $1000, calculate the PV of par...use a financial calculator, or...
1000(1.13^-9) = 1000(0.333) = 333.00

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 * 0.11 = $110
PVoa = 110[(1 - (1 / (1.13^9)) / 0.13]
= 110 *5.1317
= 564.487

add PV of par + PV of coupons = Price
333.00 + 564.487= 897.487

YOUR cash flows: Sale price - purchase price + one coupon(<you received this b/c you held the bond for one year)
897.487 - 810 + 100 = 187.487

Return before accounting for inflation = net proceeds/initial investment = 187.487 / 810 = 0.23146 or 23.146 %
the formula for Nominal rate..(1 + Nominal) = (1+Real rate)(1+inflation rate)
solving for real return...
1.23146 = (1 + Real)(1.037)
(1+Real) = 1.187522... - 1 = Real rate: 0.187522 or 18.7522%<<Real rate of returN

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