Question

(Bond price) Jump Inc has a level-coupon bond outstanding that pays 12% coupon rate and has 10 years to maturity. The face value of the bond is $1000. If the yield to maturity for similar bonds is currently 14%

a. What is the bond’s current market value if the bond pays coupons annually?

b. What is the bond’s current market value if the bond pays coupons semi-annually?

c. What is the bond’s current market value if the bond pays 14% coupons annually instead?

4. (Bond yield) A firm issues a bond today with a $1000 face value, an 8% coupon rate, and 25-year maturity.

a. An investor purchases the bond for $900, what is the YTM?

b. Suppose the investor buys the bond for $1,200 instead, what is the YTM?

c. Suppose the investor buys the bond for $1,000, what is the YTM?

d. Suppose the bond in fact pays coupons semi-annually and has a price of $820, what is the YTM?

5. (Interest Rate risk) Bond S has 3 years to maturity. Bond T has 20 years to maturity. Both have 8% coupons paid semi-annually, and are priced at par value.

a. If interest rate suddenly rises by 2%, what is the percentage change in the price of Bond S? Of Bond T?

b. If interest rate suddenly falls by 2%, what is the percentage change in the price of Bond S? Of Bond T. c. What does this problem tell you about the interest rate risk of longer-term bonds?

Answer 1

1)
a)
Face Value, FV = 1000
Annual Coupon interest, PMT = 12% * 1000 = 120
Period to Maturity, n = 10 years
Market Interest rate, i = 14%

Price = Present value of Future Cash Flows
Price = Present value of Annual Coupon + Present Value of Face Value of Maturity
Price = PMT/ i *(1 - (1+i)^-n) + FV * (1+i)^-n
Price = 120/14% *(1 - (1+14%)^-10) + 1000 * (1+14%)^-10
Price = 857.14*(1 - (1.14)^-10) + 1000 * (1.14)^-10
Price = 857.14*(1 - 0.2697) + 1000 * 0.2697
Price = 857.14*0.7303 + 1000 * 0.2697
Price = 625.93 + 269.74
Price = 895.68

b)
Face Value, FV = 1000
Semi Annual Coupon interest, PMT = 12% *(1/2) * 1000 = 60
Period to Maturity, n = 10 years or 20 Semi Years
Market Interest rate, i = 14% annually or 7% semi annually

Price = Present value of Future Cash Flows
Price = Present value of Annual Coupon + Present Value of Face Value of Maturity
Price = PMT/ i *(1 - (1+i)^-n) + FV * (1+i)^-n
Price = 60/7% *(1 - (1+7%)^-20) + 1000 * (1+7%)^-20
Price = 857.14*(1 - (1.07)^-20) + 1000 * (1.07)^-20
Price = 857.14*(1 - 0.2584) + 1000 * 0.2584
Price = 857.14*0.7416 + 1000 * 0.2584
Price = 635.64 + 258.42
Price = 894.06

c)
Face Value, FV = 1000
Annual Coupon interest, PMT = 14% * 1000 = 140
Period to Maturity, n = 10 years
Market Interest rate, i = 14%

Price = Present value of Future Cash Flows
Price = Present value of Annual Coupon + Present Value of Face Value of Maturity
Price = PMT/ i *(1 - (1+i)^-n) + FV * (1+i)^-n
Price = 140/14% *(1 - (1+14%)^-10) + 1000 * (1+14%)^-10
Price = 1000*(1 - (1.14)^-10) + 1000 * (1.14)^-10
Price = 1000*(1 - 0.2697) + 1000 * 0.2697
Price = 1000*0.7303 + 1000 * 0.2697
Price = 730.26 + 269.74
Price = 1000

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