Question

Bond & Stock Value and Evaluation. SHOW ALL FORMULAS AND SHOW ALL OF YOUR WORK. Please do not use Excel.

1. A bond with a coupon rate of 7.30% has a price that today equals $868.92. The $1.000 face value bond pays coupon every 6 months, 30 coupons remain, and a coupon was paid yesterday. Suppose you buy this bond at today's price and hold it so that you receive 20 coupons. You sell the bond upon receiving that last coupon. Find the selling price if the bond's YTM remains constant. Note that the number of coupons left is the same as "n" at the time of pricing.

Answer 1

In this question, we need to first ascertain the Yield to Maturity (YTM). The coupon rate is 7.3% which means semi-annual coupon is $36.5

semi-annual coupon, C = FV*Coupon rate / 2= $1000*7.3%/2 = $36.5

YTM can be calculated on excel using the function IRR:

For using IRR function enter the cash flows as below :

Cell A1 (t=0) : -868.92 (PV of bond i.e. cash outflow if you buy the bond)

Cell A2 to A30 (t = 1 to 29) : 36.5 (semi-annual coupon)

Cell A31 (t = 30) : 1036.5 (Face value received on maturity + last coupon)

Second argument in IRR function is a guess of coupon rate to help excel with a starting point. Taking it as 10% randomly here.

YTM = IRR (A1:A30,10%) = 4.45%

Thus YTM is 4.45% semi-annually or 8.9% annually

Now, we have to find the value of bond (or selling price) after receiving 20 coupons assuming that YTM remains same. This can be calculated using PV function in excel. After receiving 20 coupons, the number of remaining coupons (or period) will be 10. YTM remains 4.45% for each period and maturity value will be same as face value i.e. $1000.

nper = 10, rate = 4.45%, FV = $1000, PMT = $36.5

Selling price of bond = PV (4.45%, 10, 36.5, 1000,) = -$936.5 (- sign denotes cash outflow for buyer of the bond)

Thus the selling price if you sell the bond after receiving 20 coupons would be $936.5. The same result can also be achieved using FV function instead of PV function, taking number of periods as 20 and PV = current price of bond i.e. $868.92

Selling price of bond = FV (4.45%, 10, 36.5, -868.92,) = $936.5