Question

1. Suppose you have a 10% bond that pays annual coupon and with mature in 10 years. The face value is $1,000, and the yield to maturity on a similar bond is 8%.         The bond is also convertible with a conversion price of 100. The stock is currently selling for $120. What is the minimum price of the bond?

2. You are considering a project that will require an initial outlay of $200,000. This project has an expected life of five years and will generate after-tax cash flows to the company as a whole of $60,000 at the end of each year over its five-year life. Thus, the free cash flows associated with this project look like this.

Given a required rate of return of 10% percent, calculate the IRR.

Answer 1

1.

Compute the minimum price of the bond, using the equation as shown below:

Minimum price = (Interest*PVIFA_{8%, 10 years}) + (Face value*PVIF_{8%, 10 years})

                          = ($1,000*10%*6.7101) + ($1,000*0.4632)

                          = $1,134.21

Hence, the minimum price of the bond is $1,134.21.

Working note:

a.

Compute the PVIF at 8% and 10 years, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.08)¹⁰

         = 1/ 2.1589

         = 0.4632

Hence, the PVIF at 8% and 10 years is 0.4632.

b.

Compute the PVIFA at 8% and 10 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.08)^-10}/ 8%

          = (1 – 0.4632)/ 8%

            = 6.7101

Hence, the PVIFA at 8% and 10 years is 6.7101.

2.

Compute the internal rate of return (IRR), using the MS-excel as shown below:

The result of the above excel table is as follows:

Hence, the IRR is 15%.