Question

Company DEF needs advice regarding its investment decisions. Investment alternative A which the company is currently evaluating is a new machine with an initial outlay of $2,000,000, economic life of 4 years and no residual value. The machine will be related to an incremental annual revenue of $1,000,000 and incremental annual costs of $320,000. The machine will be depreciated on a straight-line basis.

Some time ago, DEF has issued bonds with total face value of $18,000,000 which pay annual coupons of 7.5% and have a maturity date in 9 years. The yield on comparable bonds in the market is 6%. DEF has a total of 4,200,000 outstanding shares with a current price of $4.21 each. The average return on the equity market index is 8.9% while the yield on government bonds is 3.2%. The company’s beta is 1.44. Furthermore, the company has 1,500,000 preference shares with a face value of $1, a coupon rate of 8% and current market price of $0.85 each. The company’s tax rate is 20%.

A. Calculate the company’s after-tax WACC.

B. Evaluate investment project A using the NPV and IRR methods of capital budgeting and provide an investment decision according to each of these criteria. Use the approximation method for calculating the IRR.

C. DEF is considering as a second alternative the project B with an initial outlay of $1,500,000 and incremental after-tax cash flows of $560,000, $460,000, $400,000, $320,000 and $300,000 for years 1 to 5, respectively. Project A and Project B are mutually exclusive. Which project should be chosen based on the constant chain of replacement assumption? Hint: Calculate the equivalent annual annuity (EAA).

Answer 1

A) Using financial calculator to calculate the present value

Inputs: N= 9

I/y= 6%

Pmt= 7.5% × 1,000 = 75

Fv= 1,000

Pv= compute

We get, present value of the bond as $1,102.03

Market value of bond = 1,102.03 × 18,000 = $19,836,540

After tax yield of bond = yield (1 - tax)

= 6% ( 1 - 0.20)

= 6% (0.80)

= 4.8%

Cost of equity = risk free rate + beta (market return - risk free rate)

= 3.2% + 1.44 (8.9% - 3.2%)

= 3.2% + 1.44 (5.7%)

= 3.2% + 8.21%

= 11.41%

Market Value of equity = 4,200,000 × 4.21 = $17,682,000

Cost of preference share = dividend / market price

= 0.08 / 0.85

= 0.0941 or 9.41%

Market value of preference share = 0.85 × 1,500,000 = 1,275,000

Total Investment = bond + equity + preference share

= 19,836,540 + 17,682,000 + 1,275,000

= $38,793,540

Weight of bond = 19,836,540 / 38,793,540 = 0.5113

Weight of equity = 17,682,000 / 38,793,540 = 0.4558

Weight of preference share = 1,275,000 / 38,793,540

= 0.0329

WACC= weight of debt × after tax cost of debt + weight of equity × cost of equity + weight of preference share × cost of preference share

= 0.5113 × 4.8% + 0.4558 × 11.41% + 0.0329 × 9.41%

= 2.45% + 5.2% + 0.31%

= 7.96%

B) cash inflow (year 1 to 4) = (sales - cost - depreciation) (1-tax) + Depreciation

= (1,000,000 - 320,000 - 500,000) (1 - 0.20) + 500,000

= (180,000) (0.80) + 500,000

= 144,000 + 500,000

= $644,000

Using financial calculator to find the NPV of project A

Inputs: C0= -2,000,000

C1= 644,000. Frequency= 4

I= 7.96%

Npv= compute

We get, Npv of the Project A as $134,910.20

IRR

Using financial calculator to calculate the IRR

Inputs: C0= -2,000,000

C1= 644,000. Frequency= 4

IRR= compute

We get, IRR of the project B as 10.953%

C) Using financial calculator to calculate the Npv

Inputs: C0= -1,500,000

C1= 560,000. Frequency= 1

C2= 460,000. Frequency= 1

C3= 400,000. Frequency= 1

C4= 320,000. Frequency= 1

C5= 300,000. Frequency= 1

I= 7.96%

We get, NPV of the project as $171,376.57

Equivalent Annual Annuity

Project A

Using financial calculator to calculate the EAA

Inputs: N= 4

I/y= 7.96%

Pv= -134,910.20

Fv= 0

Pmt= compute

We get, EAA as Project A as $40,695.94

Project B

Using financial calculator to calculate the EAA

Inputs: N= 5

I/y= 7.96%

Pv= -171,376.57

Fv= 0

Pmt= compute

We get, EAA as Project B as $42,877.13

If the projects are mutually exclusive, we should choose project B as it has higher EAA.