Rita purchased a new 40 year to maturity corporate bond at par for $5,000. The i

Question

Rita purchased a new 40 year to maturity corporate bond at par for $5,000. The issuing corporation promised to pay the bondholder $150 interest on the face value of the bond (a) If Rita sells the bond after 8 years when the prevailing bond annual coupon rate is (b) Suppose after 20 years that Rita sold the bond for $5,600, what would be the every 6 months. at 8%. How much should she expect to sell the bond for? overall effective annual yield on her investment. (Use interpolation between integer interest rates to assist in solving this problem)

Explanation / Answer

a) Calculation of Selling Price (Market Price) of the bond after 8 years of its issue (i.e. remaining term 32 years)

Price of bond is sum of present value of interest payouts and redemption amount.

Hence, price of bond = PV of Interest + PV of redemption value of bond

= 3,583.09 + 406.29

= 3,989.38

b. Calculating effective annual yield by interpolation

Effective annual yield is a discounting rate at which present value of all cash inflows is equal to initial investment ($ 5,000 in our case).

In the given question, bond is sold after 20 years i.e. after receiving interest payout of $ 150 for 40 half years.

For interpolation, we have to calculate PV of cash flows taking two different discounting rates and then calculate exact rate.

So, first calculate PV of cash flows by taking discount rate as 3.5% (7% annual).

PV of cash Flows comes to $ 4,729.78. Hence other rate is to be taken lower tha 3.5%.

Calculate PV of cash flows by taking discount rate as 3% (6% annual)

PV of cash Flows comes to $ 5,287.95

Now we will apply interpolation:

Yield (%) = 3% + (PV at 3% - 5000) / (PV at 3% - PV at 3.50%) * (3.5-3)

= 3 + (287.95 / 558.17) * 0.5

= 3 + (0.52*0.5) = 3.26%

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