Nally, Inc., is considering a project that will result in initial aftertax cash

Question

Nally, Inc., is considering a project that will result in initial aftertax cash savings of $6.9 million at the end of the first year, and these savings will grow at a rate of 3 percent per year indefinitely. The firm has a target debt-equity ratio of .68, a cost of equity of 13.3 percent, and an aftertax cost of debt of 6.3 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 percent to the cost of capital for such risky projects

Requirement 1: Calculate the WACC

Requirement 2: What is the maximum cost Nally would be willing to pay for this project?

Explanation / Answer

1) Initial aftertax cash savings of $6.9 Mn end of the first year

2) Growth rate of 3 percent per year indefinitely (i.e. its an annuity with indefinite time period or a perpetuity)

A perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. An example of when the present value of a growing perpetuity formula may be used is commercial real estate. The rental cash flows could be considered indefinite and will grow over time.

The present value of a growing perpetuity formula is the cash flow after the first period divided by the difference between the discount rate and the growth rate.

PV = CF / (r - g)

r = discount rate (in this case it will be the WACC)

g = constant growth rate

Given:  The firm has a target debt-equity ratio of .68, a cost of equity of 13.3 percent, and an aftertax cost of debt of 6.3 percent.

IF D/E = 0.68 ==> D = 0.68E ==> D/(D+E) = 0.68E/(0.68E + E) = 0.68/1.68 = 40.5%

i.e weight of Debt in total capital is D/(D+E) = 40.5% and weight of equity is 1- D/(D+E) = 1- 0.405 = 59.5% = E/ (D+E)

Now WACC = (weight of Debt * after tax cost of debt) + (weight of equity * cost of equity)

= 40.5% * 6.3% + 59.5% * 13.3% = (0.405* 6.3) + (0.595* 13.3) = 10.47% ~ 10.5%

But, the cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 percent to the cost of capital for such risky projects

Therefore the discount rate used = WACC + 2% = 10.5% + 2% = 12.5%

The maximum cost Nally would be willing to pay for this project will be the PV of all the future cash flows with constant growth rate of 3% and using a discount rate of 12.5%. Paying over and above this will be like buying it at a premium without justification.

So, PV of perpetuity = 6.9 /(12.5% - 3%) = 6.9/9.5% = 6.9/0.095 = $ 72.63 Mn

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