Question

You bought one of Great White Shark Repellant Co.’s 8 percent coupon bonds one year ago for $1,044. These bonds make annual payments and mature 13 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 6 percent. The bonds have a par value of $1,000.Required:If the inflation rate was 3.4 percent over the past year, what was your total real return on investment?

Answer 1

The total real return on investment is 8.41%.

Step-by-step explanation:

The total real return on investment can be calculated by considering the effects of inflation on the nominal return. In this case, the nominal return is the difference between the selling price of the bond and the purchase price, plus any interest payments received. The selling price of the bond is calculated as the present value of the future cash flows, discounted at the required return of 6 percent. The purchase price of the bond is given as $1,044, and the interest payments can be calculated as 8 percent of the par value of $1,000 for each year. Therefore, the nominal return is the sum of the selling price, interest payments, and the par value.

To calculate the total real return, we need to adjust the nominal return for inflation. The total real return is given by the equation:

Total Real Return = (1 + Nominal Return) / (1 + Inflation Rate) - 1

Plugging in the values, the total real return is:

Total Real Return = (1 + 0.12) / (1 + 0.034) - 1 = 0.0841 or 8.41%

Answer 2

17.4%

Step-by-step explanation:

original purchase price 1 year ago = $1,044

current market price:

0.06 = {80 + [(1,000 - MV)/13]} / [(1,000 + MV)/2]

0.06 x [(1,000 + MV)/2] = 80 + [(1,000 - MV)/13]

0.06 x (500 + 0.5MV) = 80 + 76.92 - 0.0769MV

30 + 0.03MV = 156.92 - 0.0769MV

0.1069MV = 126.92

MV = 126.92 / 0.1069 = $1,187.28

total returns during the year = $80 (coupon) + ($1,187.28 - $1,044) = $223.28

nominal return on investment = $223.28 / $1,044 = 21.387%

real return on investment = [(1 + i) / (1 + inflation)] - 1 = [(1 + 0.21387) / (1 + 0.034)] - 1 = 1.174 - 1 = 0.174 = 17.4%