Question

Spacely’s Sprockets wants to raise funding to develop software for a new Space Transport System. They have chosen to pursue debt financing and will sell bonds. Assume the following regarding their funding:

• The company needs to raise $500,000 for the project
• They will pay a 5% coupon annually
• The bond’s yield-to-maturity is 4%
• The bond will last 5 years
• The risk-free rate of return is 3% annually

1. What is the price of the bond? (4 points)
2. Assume the yield-to-maturity changes from 4% to 7 %. What is the bond’s price change (in percentage) in reaction to this change in yield? (4 points)
3. What is the Duration of this bond (assume interest rates are once again at 4%)? (5 points)
4. What is the Modified Duration of this bond? (4 points)
5. What is the Duration approximated change in the value of the bond if the yield increases from 4% to 7%? (4 points)
6. What is the Convexity of this bond? (5 points)
7. What does Convexity Measure? (4 points)
8. Now, incorporate convexity to calculate the approximated change in the price of the bond if the yield increases from 4% to 7%. (5 points)

Answer 1

price of bond has been calculated using PV function of EXCEL

duration is the weighted average maturity of the bond , to calculate the same a table is constructed

the weights used are , Present value of cash flows of bond/price of bond

these weights are then multiplied by the time until the payment (t) , the sum of the product of t and the weights gives the duration

for convexity we first find (t^2)+t , and then multiply this with the present value of cash flows ,

convexity =(sum of product found above for each t)/(price of bond *((1+ytm)^2))

1 amount needed 2 yield to maturity(YTM) 3 time to maturity 4 coupon rate 5 coupon value 6 risk free rate 7 1 8 price of bond 9 2) 10 new YTM 11 new price of bond 12 % price change 13 3) 14 duration 15 4) 16 modified duration 17 5 18 % change in price 19 6) 20 convexity 21 7) convexity like duration measures the interest rate risk of a bond and is a better predictor of the same than duration period time until payment, t cash flow PV of CF weight, wt w (t 2)+column J column G 500000 0.04 125000 24038.460.046028 0.046028 2 25000 23113.91 0.044258 0.088515 25000 22224.91 0.042555 0.127666 25000 21370.1 0.0409190.163674 51 5250001 431511.71 0.826241| 4.131203 48076.92308 138683.432 266698.9076 427402.0955 12945351.93 0.05 12 20 30 4 4 0.03 522259.11 0.07 458998.03 12.11% 4.56 4.38 13.15% 24.48 23 approximate change in -12.04%

1 amount needed 2 yield to maturity (YTM) 3 time to maturi 4 coupon rate 5 coupon value 500000 period time until payment, t cash flow PV of CF weight, wtw (t*2)+tcolmn J*column G SBS5 $B$5 SB$5 0.04 0.05 B4 B1 0.03 risk free rate 8 price of bond 9 2) 10 new YTM 11 new price of bond 12 % price change 13 3) 14 duration 15 4) 16 modified duration 17 5) 18% change in price 19 6) 20 convexity 21 7) convexity like duration mea -PV(B2,SB$3,$8$5,SB$1) 0.07 (811-B8)/B8 -SUM(12:16) -B14/(1+B2) -B16 (B10-B2 SUM(K2:K6)/(B8(1+B2)A2)) 23 approximate change in price B18+(0.5 B20*( (B10-B2)42))