Question

In: Finance

Consider a newly issued TIPS bond with a three year maturity, par value of $1000, and...

Consider a newly issued TIPS bond with a three year maturity, par value of $1000, and a coupon rate of 7%. Assume annual coupon payments.

Time

Inflation in year just ended

Par Value

Coupon Payments

Principal Payment

Total Payment

0

$1000.00

1

3.0%

2

3.5%

3

4.5%

a) Fill in the shaded cells with amounts in the above table.

b) What is the nominal rate of return on the TIPS bond in the first year?

c)      What is the real rate of return on the TIPS bond in the first year?

Solutions

Expert Solution

Part a)

The completed table is provided as follows:

Time Inflation in year just ended Par Value Coupon Payments Principal Payment Total Payment
0 $1,000.00
1 3.0% $1,030.00 [1,000*(1+3.0%)] $72.10 [1,030.00*7%] $0 $72.10 [72.10 + 0]
2 3.5% $1,066.05 [1,030*(1+3.5%)] $74.62 [1,066.05*7%] $0 $74.62 [74.62 + 0]
3 4.5% $1,114.02 [1,066.05*(1+4.5%)] $77.98 [1,114.02*7%] $1,114.02 $1,192.00 [77.98 + 1,114.02]

______

Part b)

The nominal rate of return on the TIPS bond in the first year is determined as below:

Nominal Rate of Return = (Price at the End of Year - Price at the Beginning of the Year + Coupon Payment)/Price at the Beginning of the Year*100

Substituting values in the above formula, we get,

Nominal Rate of Return (First Year) = (1,030 - 1,000 + 72.10)/1,000*100 = 10.21%

______

Part c)

The real rate of return is arrived as follows:

Real Rate of Return = (1+Nominal Rate of Return)/(1+Inflation Rate) - 1

Substituting values in the above formula, we get,

Real Rate of Return (First Year) = (1+10.21%)/(1+3%) - 1 = 7%


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