You bought one of Great White Shark Repellant Co.’s 8.5 percent coupon bonds one

Question

You bought one of Great White Shark Repellant Co.’s 8.5 percent coupon bonds one year ago for $1,064. These bonds make annual payments and mature 11 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 6 percent.

If the inflation rate was 3.8 percent over the past year, what was your total real return on investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

If the inflation rate was 3.8 percent over the past year, what was your total real return on investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

B0 = the bond price,
C = the annual coupon payment, = $1,000 x 8.5% = $85
F = the face value of the bond, = $1,000
YTM = required return on bond, = 6%
t = the number of years remaining until maturity = 11Years

Bond Value = C {[1-(1+(YTM))-t/(YTM)] + [F / (1+ (YTM))t]
=> $85{[1-(1+0.06)-11/(0.06)] + [$1,000 / (1+(0.06)11] = $1,197

Cash Flow from the bond = Sale price - purchase price + one coupon(<you received this b/c you held the bond for one year)

Return before accounting for inflation = net proceeds/initial investment = $218 / $1,064 = 0.20488 or 20.49%
the formula for Nominal rate=> (1 + Nominal) = (1+Real rate)(1+inflation rate)
solving for real return...
1.2049 = (1 + Real)(1.038)
(1+Real) = 1.16078
Real rate = 1 – 1.16078 = 0.16078 or 16.08%

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