Question

Question 1. (Interest Rates and Bond Valuation)

(1) Find out values of following bonds. YTM is 7%, and Time to maturity is 10 years

Bond A: 3.5% of coupon paid semiannually, Face value = $1,000,000 Bond B: 0% of coupon, Face value = $5,000,000
Bond C: 10% of coupon paid annually, Face value = $3,500,000

(2) Suppose you will receive money of $ 20,000 worth of purchasing power for 5 years. The first payment will be given at the end of this year. Assuming the inflation rate is 10% and nominal discount rate is 15%, what is the present value of these cash flows? Provide answer in two ways.

1) Discount nominal cashflows with nominal rates

2) Discount real cashflows with real rates Hint: Use Fisher Effect

Answer 1

Part 1)

Given :

YTM = 7%

Time to maturity = 10 years

Bond A:

Coupon rate - 3.5% paid semiannually (Since the question says, '3.5% of coupon paid semiannually, we presume that the annual rate is 7% and 3.5% is paid semiannually)

Face value = $1,000,000

Value of bond A = PV of coupons paid + PV of face value

PV of coupons: 3.5% of 1,000,000 = 35,000$

35,000(1/1.07+1/1.07^2...........+1/1.07^20) [As coupon is paid semiannually, time = 10 years * 2 = 20 periods, YTM = 7%]

Solving using excel:

Thus, PV of coupon = 370,790$

PV of face value: 1,000,000/1.07^10 = 508349.29$

Thus value of the bond = 370,790 + 258,419 = 879,139.29$

Bond B:

Face value = 5,000,000$

Value of bond B = PV of Face value ( as it is a zero coupon bond)

Value of bond B = 5,000,000/(1+0.07)^10 = 5,000,000/1.07^10 = 2,541,746.46$

Bond C:

Face value = 3,500,000$

Coupon rate = 10% annually

Value of bond C = PV of coupons paid + PV of face value

PV of coupons: 10% of 3,500,000 = 350,000$

350,000(1/1.07+1/1.07^2...........+1/1.07^10)

Solving using excel:

Thus, PV of coupon = 2,458,254$

PV of face value: 3,500,000/1.07^10 = 1,779,222.52$

Thus value of the bond = 2,458,254 + 1,779,222.52 = 4,237,476.52$

Part 2)

Amount - 20,000$

Time - 5 years

Inflation rate - 10%

Nominal discount rate - 15%

1. Discount nominal cash flows with nominal rate:

We need to first calculate the nominal cash flows, this can be done using the following formula:

Nominal cash flow = Real Cash flow * (1+Inflation Rate)^t

The cash flows are then discounted using the nominal discount rate and the formula:

PV = Cash flow/(1+nominal rate)^t

Solving this using excel:

Thus, present value using this method is: 87,688.4$

2.Discount real cashflows with real rates:

To find the real discount rate:

Nominal discount rate = (1+real discount rate)(1+inflation rate) - 1

0.15 = (1+ x)(1+0.1)-1

1.15 = (1+x)*1.1

1.15/1.1 = 1+x

1.0455 = 1+x

x = 0.455 or 4.55%

Thus, we use the above rate to discount the cash flows and find the PV with the folowing formula:

PV = Cash flow/(1+rate)^t

Solving using excel:

Thus, PV = 87,688.4$

Tip: While solving using excel, dont use real rate as 4.55%, but type in the formula (1.15/1.1) - 1 to get the exact answer.