Question

Sarah owns investment A and 1 bond B. The total value of his holdings is $2,200. Investment A is expected to pay annual cash flows to Sarah of $200 per year with the first annual cash flow expected later today and the last annual cash flow expected in 5 years from today. Investment A has an expected return of 17.40 percent. Bond B pays semi-annual coupons, matures in 19 years, has a face value of $1000, has a coupon rate of 9.80 percent, and pays its next coupon in 6 months. What is the yield-to-maturity for bond B? 5.58% (plus or minus 0.04 percentage points) 6.44% (plus or minus 0.04 percentage points) 5.80% (plus or minus 0.04 percentage points) 2.90% (plus or minus 0.04 percentage points) None of the above is within 0.04 percentage points of the correct answer

Answer 1

First, we will calculate the Present value of future cash flows of Investment A:

Year	Cash Flows ($)	PV Factor @17.40%	Present Value ($)
0	200.00	1.0000	200.00
1	200.00	0.8518	170.36
2	200.00	0.7255	145.11
3	200.00	0.6180	123.60
4	200.00	0.5264	105.28
5	200.00	0.4484	89.68
		Present value	834.03

Present Value of Investment A = $834.03

Total value of Holding consisting of Investment A and 1 bond B = $2200

Current Value of Bond B + Value of Holding - Current value of Investment A

= $ 2200-$834.03

= $ 1365.97

Bond B;

Face value of bond = $1000

Semi-annual coupon rate = 9.8%

Semi-annual coupon payment = $1000*9.8%*1/2 =$49

Maturity = 19 years

n = 19*2 = 38 (being semiannual coupon payment)

Calculating YTM of the bond using IRR technique:

First, taking YTM as 6%

semi-annual Ytm = 6%/2 = 3%

Value = - Coupon Payment (1+YTM)" - Coupon Payment Coupon Payment 2 +..... (1+YTM) (1+YT M FaceValue (1 + YTM +

49 49 49 1000 Price = (1 +0.03)1 + (1 +0.03)2 + ... + (1+0.03)35 + (1 +0.03)3

Value = $1102.13 + $ 325.23

Value = $ 1427.36

Since, value at YTM 6% is very close and higher than the original price. Now increasing YTM to  7%

Semi-annual ytm = 7%/2 =3.5%

Value = - Coupon Payment (1+YTM)" - Coupon Payment Coupon Payment 2 +..... (1+YTM) (1+YT M FaceValue (1 + YTM +

49 49 (1 + 0.035)1" (1 + 0.035)2 49 1000 (1 +0.035)38' (1 + 0.035)38

Value = $1021.21 + $ 270.56

Value = $ 1291.77

Calculating YTM based on above Value at different rates:

YTM = Lower Rate ValueLR - CurrentValue *(Higher Rate-Lower Rate) Value - ValueHR

YTM = 6+ (1427.36 – 1365.97) ** (7-6) (1427.36 – 1291.77)

YTM = 6.45%

Hence, Option B

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