Question

Price Current Yield Problem 2: (20 points) Suppose you hold a 6.5 percent coupon bond with a par value of $100 that matures in 14 years and pays semi-annual coupons. 1) If currently, the bond is priced to offer a yield to maturity of 7.2 percent, what is its current selling price? 2) You believe that in one year, the yield to maturity will be 6.8 percent. a. Will the bond price increase or decrease from its current market value? Explain why. (No Calculations required) b. Will the price be higher or lower than $100? Explain why. (No calculations required). 3) If you hold the bond for the entire year and the change in yield to maturity occurs, what would be your total return in dollars and percentage? www.euruni.edu

Answer 1

We have following information about Bond

Par value = $ 100

Coupon rate = 6.5 %

Maturity = 14 years

Pays semi-annual coupons.

1.

Price of Bond is equals to Present value of all cash inflows at discounted at YTM.

Please refer below spreadsheet for Calculation of Price of Bond when YTM is 7.2 %

N19 3.250%) Semi annual 28 semi-annual PVF (3.60%) 1 0.965250965 2 0.931709426 3 0.899333423 4 0.868082454 50.837917427 6 0.808800605 70.780695565 80.753567148 9 0.727381417 10 0.702105614 11 0.677708122 12 0.654158419 13 0.631427045 14 0.609485565 150.58830653 16 0.567863446 170.548130739 18 0.529083725 19 0.510698576 20 0.492952294 21 0.475822677 22 0.459288299 23 0.443328474 24 0.427923237 25 0.413053318 26 0.398700114 27 0.384845669 28 0.371472654 Coupon rate Maturit Par value year 100.00 4 3.60%) semi annual Year Cash Flow PVF(3.60% Present Value 3.25 100.00 Price of Bond 17.459 S 0.371 $ 56.74 37.15 93.89 1-28 10 28 12 13 16 17 18 19 21 23 25 27 30 Annuity factor 17.45909295

Formula reference-

Thus, Price of Bond would be $ 93.89.

2. Yield to Maturity in one year is 6.8 %

(a) The price of Bond is inversely related to the interest rate (YTM), Thus, Price of Bond increase in one year as YTM reduced from 7.2% to 6.8%.

(b) When coupon rate is equal to YTM rate then Price of Bond also equals to Par value of Bond and When coupon rate is less than YTM rate then Price of Bond also less than Par value of Bond and vice versa.

In our case, Coupon rate is 6.5 % and reduced YTM in one year is 6.8%. YTM rate is still greater than coupon rate, Thus, Price of Bond would be lower than $ 100.

3. Return of Bond at the end one year.

Firstly, we calculate Price of Bond at the end of one year at YTM rate 6.8%.

Formula Reference -

C4 Cou Maturit Par value YTM rate Semi annual PVF (3.40% 14 2 semi-annual -6.8%/2 semi annual Cash Flow C3 C1 -C3 PVF(3.40% -H30 -H29 Present Value -C9 D9 -C10 D10 -SUM(E9:E10 Year 1-28 10 28 G10 Price of Bond 10 1/(1+SC$4) G12 1/(1+SC$4) G13 13 14 1/1+SCS4)AG15 1/(1+SC$4)AG16 1/1+$C$4) G17 1/(1+SC$4) G18 1/(1+SC$4) G19 1/(1+$C$4) G20 1/1+SCSA) G21 1/(1+SC$A) G22 1/(1+SC$4) G23 1/(1+SC$4) G24 17 16 17 18 19 21 23 24 26 27 G26 +SCSA)G27 1/(1+SC$A)AG28 26 27 28 Annuity factor 29 SUM(H2:H29ows Goto Settings to a WndowS

Thus, Price of Bond at year end is $ 97.32

$Return on Bond in one year = \frac{C+(BV_{1}-BV_{0})}{BV_{0}}$

where,

C = Coupons

BV₁ = Bond value at end of year

BV₀ = Bond value at beginning

Return of Bond = {6.5 + (97.32 - 93.89)}/97.32

= 9.93/97.32

= 0.1020 or 10.20%

Thus, After one Year, Total Return would be $ 9.93 and Rate of Return would be 10.20%