Suppose you purchase a ten-year bond with 6% annual coupons.  You hold the bond for four years and sell it immediately after receiving the fourth coupon.  If the bond's yield to maturity was 5% when you purchased and sold the bond.

a.  What cash flows will you pay and receive from your investment in the bond per $100 face value?

We need to calculate how much we are willing to pay for the bonds by using the formula as follows: -

where B is the issued price

C is the coupon payment

r is the discount or yield rate

n is the period

C, which is the annual coupon payment, can be calculated by multiplying $100 with 6%. We will get $6 coupon payment.

The price of the bond is equal to

B = 6 x [1 - 1 ] + 100

(1 + 0.05)⁴ (1 + 0.05)⁴

0.05

B = $103.55

We will be willing to pay for the bond at $103.55.

Then, we will need to find the price that we will be able to sell at the end of year 4 whereby the maturity of the bond is only 6 years left.

B = 6 x [1 - 1 ] + 100

(1 + 0.05)⁶ (1 + 0.05)⁶

0.05

B = $105.08

The cash flows I will receive in total is $129.08 [($6 x 4 years) + $105.08].

b.  What is the internal rate of return of your investment?

The internal rate of return is defined as that discount rate which equates the present value of a project's expected cash inflows to the present value of the project's costs:

PV(Inflows) = PV(Investment costs), or the rate which makes the NPV to equal zero.

NPV = sum of CF_t where CF is the cash flow

(1 + IRR)^t IRR is the internal rate of return

t is the period.

The decision rule as to whether the project will be accepted for IRR is when the project’s IRR is greater than the company’s cost of capital.

NPV = -103.55 + 6 + 6 + 6 + 129.08 = 0

(1+IRR)¹ (1+IRR)² (1+IRR)³ (1+IRR)⁴

IRR =  9.87%

Calculating for IRR is a trial and error procedure. Therefore, it is easier to use a financial calculator to compute IRR or IRR calculation function in excel to calculate for us. Please see the attached excel file.

Year 0	- 103.55
1	6.00
2	6.00
3	6.00
4	129.08
IRR =	9.87%