Question

8. You have just received an inheritance of $20,000. You wish to invest in fixed income securities such as bonds, which you think are less risky than stocks. After some research, you have narrowed down your choices to the following three fixed income securities:

One-year Treasury Bill:

Face value of $1000
Yield to maturity of 1.74%

Coupon Bond A:

Two years to maturity
Face value of $1000
Coupon rate of 3%, with semi-annual coupon payments
Price multiple of face value = 1.0189

Coupon Bond B:

Five years to maturity
Face value of $1000
Coupon rate of 3.5%, with annual coupon payments
Yield to maturity of 2.51%

All yields to maturity are compounded semi-annually.                              (9 marks total)

1. What is the price of the one-year treasury bill?                                 (2 marks)
2. What is the yield to maturity on Coupon Bond A?                              (2 marks)
3. What is the price of Coupon Bond B?                                              (2 marks)
4. If the inflation rate is 1.5%, what are the real yields on the one-year treasury bill, Coupon Bond A, and Coupon Bond B?         (2 marks)
5. If your personal real hurdle rate (the minimum rate of return required on investments) is 1%, which of the three fixed income securities would you choose to invest in?                                                        (1 mark)

Answer 1

a]

Price of bill = face value / (1 + YTM)^{years to maturity}

Price of bill = $1000 / (1 + 1.74%)^{years to maturity}

Price of bill = $982.90

b]

YTM is calculated using RATE function in Excel with these inputs :

nper = 2*2 (2 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 3% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1000 * 1.0189 (current bond price = face value * price multiple of face value. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 1.02%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 2.03%

A1 - х v f =RATE(2*2,1000*3%/2,-1000*1.0189,1000)*2 B C D A 2.03%| 1

c]

Price of bond is calculated using PV function in Excel :

rate = 2.51% (YTM of bond)

nper = 5 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 3.5% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,045.98

A2 x fac =PV(2.51%,5,1000*3.5%, 1000) B C D E F A 2 ($1,045.98)

d]

(1 + real yield) = (1 + nominal yield) / (1 + inflation rate)

1-year bill

(1 + real yield) = (1 + nominal yield) / (1 + inflation rate)

(1 + real yield) = (1 + 1.74%) / (1 + 1.5%)

real yield = (1.0174 / 1.015) - 1 = 0.2365%

Bond A

(1 + real yield) = (1 + nominal yield) / (1 + inflation rate)

(1 + real yield) = (1 + 2.03%) / (1 + 1.5%)

real yield = (1.0203 / 1.015) - 1 = 0.5222%

Bond B

(1 + real yield) = (1 + nominal yield) / (1 + inflation rate)

(1 + real yield) = (1 + 2.51%) / (1 + 1.5%)

real yield = (1.0251 / 1.015) - 1 = 0.9951%

e]

None of the securities should be chosen as the real yield of all the securities is below the hurdle rate of 1%.