Question

1. A bond has 10% coupon rate (coupon paid semiannually) and it has 10 years left to maturity. The face value is $1000. If the bond currently sold for $1100.

1. What is the yield to maturity?
2. If suddenly the interest rate decreases 2%, what is the new bond price? What is the percentage change of bond price?

Answer 1

a. We can use the IRR function in excel to calculate the Yield to maturity of the bond

Period	Cash Flows	Explanation
0	-1100	Bond purchase price, Negative sign for Cash outflow to purchase it
1	50	Semi annual coupons = 1000*10%/2 = $50
2	50
3	50
4	50
5	50
6	50
7	50
8	50
9	50
10	50
11	50
12	50
13	50
14	50
15	50
16	50
17	50
18	50
19	50
20	1050	The last Half yearly coupon + The par value received
IRR half yearly	4.25%	IRR Function taking all values of cash flow beginning from -1100 to 1050
Annual IRR	8.50%	Multiplying the half yearly IRR by 2

Alternatively

This can also be calculated using the Rate function inn excel,

Here,

NPER = 20 (Semi annual periods)

PMT = Coupons = Par value X Coupon Rate X 1/2 = 1000 X 10% x 2 = $50 (Since semi annual)

PV = Purchase price of Bond = - $1100 (Negative sign indicates purchase, cash outflow)

FV = Par value to be received at end = $1000

Type = 0, (Payment at the end of period, First coupon received 6 months from start date)

Thus Rate = Rate (20,50,-1100,1000,0) = 4.25%

Annual Rate or YTM = 2 x 4.25% = 8.50%

B, If the rate of interest decreases by 2%, the bond will find a price, so that the yield to maturity (YTM) is 2% less than what it was previously.

Using the excel function of PV, we will find the current price of the bond.

Here,

Rate = 8,5% -2.0% = 6.50% /2 = 3.25% (Since semi annual rate)

NPER = Payment period of coupons = 20 (20 semi annual payments)

PMT = Semi annual Coupons = Par value X Coupon Rate X 1/2= 1000 x 10% x 1/2 = 50

FV = The value bond will pay back at the end of 20 periods, the par value = 1000

Type = 0 (Payment at the end of period, First coupon received 6 months from start date)

Using above in Excel,

we get PV = PV(3.25%,20,50,1000,0) = -$1,254.44 (Negative sign indicates cash outflow, purchase price)

  B. The percentage change = (Previous value - Current Price) / Previous price

= (1100 - 1254)/ 1100 = -154/1100 = 14.04%

The bond value is now $1254, a 14.04% higher than previously.