Question 18.1: A C corporation is looking at investing in one of two invest...
A C corporation is looking at investing in one of two investments. Both investments have a before-tax cash flow of -$20,000 for the first year and a before-tax cash flow of $40,000 for the second year. The first investment is a passive investment and the losses from the first year must be carried forward to the second year. For the second investment, the company may write the first year’s losses off against other income earned by the company during the first year. Using a marginal tax rate of 34% and a MARR of 15% compare the net present values of the after-tax cash flows for these two investments. How do the after-tax net present values compare to the before-tax net present values?
No tax savings occur during the first year for the first investment because the loss must be carried forward. The taxable income for the second year is $20,000 ($40,000 – $20,000). The tax liability for the second year is as follows:
Tax_2 = $20,000(0.34) = $6,800
The after-tax cash flows for the first investment are as follows:
Cash Flow1 = -$20,000
Cash Flow2 = $40,000 – $6,800 = $33,200
The net present value for the first investment is calculated using Eq. (15-3) as follows:
P = F/(1 + i)^n (15-3)
NPV = -$20,000/(1 + 0.15)^1 + $33,200/(1 + 0.15)^2 = $7,713
The second investment may take the tax savings in year 1. The tax liabilities for the second investment are as follows:
Tax_1 = -$20,000(0.34) = -$6,800
Tax_2 = $40,000(0.34) = $13,600
The after-tax cash flows for the second investment are as follows:
Cash Flow_1 = -$20,000 + (-$6,800) = -$13,200
Cash Flow_2 = $40,000 – $13,600 = $26,400
The net present value for the second investment is calculated using Eq. (15-3) as follows:
NPV = -$13,200/(1 + 0.15)^1 + $26,400/(1 + 0.15)^2 = $8,484
The before-tax net present value for both investments is calculated using Eq. (15-3) as follows:
NPV = -$20,000/(1 + 0.15)^1 + $40,000/(1 + 0.15)^2 = $12,854
The net present value of the first investment is $771 ($8,484 – $7,713) less than the net present value of the second investment because the company had to carry the first year loss forward. Taxes reduce the net present value of the first investment by $5,141 ($12,854 – $7,713) and the net present value of the second investment by $4,370 ($12,854 – $8,484).