Question

Amazing Manufacturing, Inc., has been considering the purchase of a new manufacturing facility for $580,000. The facility is to be fully depreciated on a straight-line basis over seven years. It is expected to have no resale value at that time. Operating revenues from the facility are expected to be $430,000, in nominal terms, at the end of the first year. The revenues are expected to increase at the inflation rate of 4 percent. Production costs at the end of the first year will be $275,000, in nominal terms, and they are expected to increase at 5 percent per year. The real discount rate is 7 percent. The corporate tax rate is 24 percent.

   

Calculate the NPV of the project. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Given

Purchase cost of new manufacturing facility = $580,000

Operation revenues = $430,000 in year1 with 4% increase every year

Production cost = $275,000 in year1 with 5% increase every year

The above given cashflows are nominal cashflows

But the discount rate of 7% is real discount rate. So, to calculate NPV we convert the real discount rate into nominal discount rate by using the formula

(1+real discount rate)$\times$(1+inflation rate) = (1+nominal discount rate)

(1+0.07)$\times$(1+0.04) = (1.1128) = (1+nominal discount rate)

Nominal discount rate = 1.1128-1 = 0.1128

$\therefore$ Nominal discount rate = 11.28%

Depreciation per annum = $580,000 $\div$ 7years =$82857.14

Computation of NPV

Particulars	Year 1	Year 2	Year3	Year 4	Year 5	Year 6	Year 7
Revenues	$430,000	$447,200	$465,088	$483,691.52	$503,039.1808	$523,160.748	$544,087.1779
Production costs	$275,000	$288,750	$303,187.5	$318,346.875	$334,264.2187	$350,977.4296	$368,526.3011
Depreciation	$82,857.14	$82,857.14	$82,857.14	$82,857.14	$82,857.14	$82,857.14	$82,857.16
Profit before Tax	$72,142.86	$75,592.86	$79,043.36	$82,487.505	$85,917.8221	$89,326.1784	$92,703.7168
Tax @ 24%	$17,314.2864	$18,142.2864	$18,970.4064	$19,797.0012	$20,620.2773	$21,438.2828	$22,248.8920
Profit after Tax	$54,828.5736	$57,450.5736	$60,072.9536	$62,690.5038	$65,297.5448	$67,887.8956	$70,454.8248
Add: Depreciation	$82,857.14	$82,857.14	$82,857.14	$82,857.14	$82,857.14	$82,857.14	$82,857.16
Cashflows after tax	$137,685.7136	$140,307.7136	$142,930.0936	$145,547.6438	$148,154.6848	$150,745.0356	$153,311.9648
PvF(11.28%,n)	0.899	0.807	0.726	0.652	0.586	0.527	0.473
Present value of cash inflows	$123,779.456	$113,228.3248	$103,767.2479	$94,897.0638	$86,818.6452	$79,442.6338	$72,516.5593

NPV = Present value of cash inflows - Present value of cash outflows

= $674,449.9308 - $580,000 = $94,449.93

Since NPV is positive, company can take up the new manufacturing facility