In: Finance
Please show all work.
Mahya Fashions Inc. can invest $5 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 5 million jars of make-up a year. Fixed costs are $2 million a year, and variable costs are $1 per jar. The product will be priced a $2 per jar. Plant requires $50,000 in additional net working capital. The plant will be depreciated straight-line over 5 years to a salvage value of $50,000. Using the WACC you have found above and the tax rate of 20 percent, please answer the following:
a. What is project NPV and IRR under these base-case assumptions? Accept or Reject?
b. What is NPV if variable costs turn out to be $1.20 per jar?
c. What is NPV if fixed costs turn out to be $1.5 million per year?
d. At what price per jar would the project NPV equal zero?
a] | INITIAL INVESTMENT: | |
Cost of the plant | $ 5,000,000 | |
+Net working capital | $ 50,000 | |
=Initial investment | $ 5,050,000 | |
ANNUAL OPERATING CASH FLOWS: | ||
Sales =5000000*2 = | $ 10,000,000 | |
-Variable costs =5000000*1= | $ 5,000,000 | |
-Fixed Costs | $ 2,000,000 | |
-Depreciation = (5000000-50000)/5 = | $ 990,000 | |
=NOI | $ 2,010,000 | |
-Tax at 20% | $ 402,000 | |
=NOPAT | $ 1,608,000 | |
+Depreciation | $ 990,000 | |
=Annual operating cash flow | $ 2,598,000 | |
TERMINAL NON-OPERATING CASH FLOWS: | ||
After tax salvage value | $ 50,000 | |
[No tax as Book value=Sale value] | ||
Recovery of NWC | $ 50,000 | |
Terminal non-operating cash flows | $ 100,000 | |
CALCULATION OF NPV: | ||
PV of annual cash flows = 2598000*(1.104^5-1)/(0.105*1.105^5) = | $ 9,723,946 | |
PV of terminal non-operating cash flows = 100000/1.105^5 = | $ 60,700 | |
Total PV of cash inflows | $ 9,784,646 | |
Less: Initial investment | $ 5,050,000 | |
NPV | $ 4,734,646 | |
CALCULATION OF IRR: | ||
IRR is that discount rate for which NPV = 0. It has to be found out | ||
Discount rate of 43%: | ||
PV of annual cash flows = 2598000*(1.43^5-1)/(0.43*1.43^5) = | $ 5,031,467 | |
PV of terminal non-operating cash flows = 100000/1.43^5 = | $ 16,723 | |
Total PV of cash inflows | $ 5,048,190 | |
Less: Initial investment | $ 5,050,000 | |
NPV | $ (1,810) | |
Discount rate of 42%: | ||
PV of annual cash flows = 2598000*(1.42^5-1)/(0.42*1.42^5) = | $ 5,114,323 | |
PV of terminal non-operating cash flows = 100000/1.42^5 = | $ 17,320 | |
Total PV of cash inflows | $ 5,131,643 | |
Less: Initial investment | $ 5,050,000 | |
NPV | $ 81,643 | |
As 0 NPV falls between 42% and 43%, IRR also falls between those | ||
rates. | ||
By simple interpolation, IRR = 42%+1%*81643/(81643+1810) = | 42.98% | |
b] | ANNUAL OPERATING CASH FLOWS: | |
Sales =5000000*2 = | $ 10,000,000 | |
-Variable costs =5000000*1.2= | $ 6,000,000 | |
-Fixed Costs | $ 2,000,000 | |
-Depreciation = (5000000-50000)/5 = | $ 990,000 | |
=NOI | $ 1,010,000 | |
-Tax at 20% | $ 202,000 | |
=NOPAT | $ 808,000 | |
+Depreciation | $ 990,000 | |
=Annual operating cash flow | $ 1,798,000 | |
PV of annual cash flows = 1798000*(1.105^5-1)/(0.105*1.105^5) = | $ 6,729,659 | |
PV of terminal non-operating cash flows = 100000/1.105^5 = | $ 600,930 | |
Total PV of cash inflows | $ 7,330,589 | |
Less: Initial investment | $ 5,050,000 | |
NPV | $ 2,280,589 | |
c] | ANNUAL OPERATING CASH FLOWS: | |
Sales =5000000*2 = | $ 10,000,000 | |
-Variable costs =5000000*1= | $ 5,000,000 | |
-Fixed Costs | $ 1,500,000 | |
-Depreciation = (5000000-50000)/5 = | $ 990,000 | |
=NOI | $ 2,510,000 | |
-Tax at 20% | $ 502,000 | |
=NOPAT | $ 2,008,000 | |
+Depreciation | $ 990,000 | |
=Annual operating cash flow | $ 2,998,000 | |
PV of annual cash flows = 2998000*(1.105^5-1)/(0.105*1.105^5) = | $ 11,221,089 | |
PV of terminal non-operating cash flows = 100000/1.105^5 = | $ 600,930 | |
Total PV of cash inflows | $ 11,822,019 | |
Less: Initial investment | $ 5,050,000 | |
NPV | $ 6,772,019 | |
d] | For 0 NPV, the PV of total after tax annual sales for | |
the 5 years should be lower by the NPV of $4860556. | ||
Therefore, annual after tax sales should be lower by = 4860556*0.105*1.105^5/(1.105^5-1) = | $ 1,298,621 | |
Before tax annual sales should be lower by = 1298621/0.80 = | $ 1,623,277 | |
Price per jar should be lower by 1623277/5000000 = | $ 0.3247 | |
Therefore, price for NPV = 2-0.3247 = | $ 1.6753 | |
VERIFICATION: | ||
ANNUAL OPERATING CASH FLOWS: | ||
Sales =5000000*1.68 = | $ 8,400,000 | |
-Variable costs =5000000*1.0= | $ 5,000,000 | |
-Fixed Costs | $ 2,000,000 | |
-Depreciation = (5000000-50000)/5 = | $ 990,000 | |
=NOI | $ 410,000 | |
-Tax at 20% | $ 82,000 | |
=NOPAT | $ 328,000 | |
+Depreciation | $ 990,000 | |
=Annual operating cash flow | $ 1,318,000 | |
PV of annual cash flows = 1318000*(1.105^5-1)/(0.105*1.105^5) = | $ 4,933,087 | |
PV of terminal non-operating cash flows = 100000/1.105^5 = | $ 60,700 | |
Total PV of cash inflows | $ 4,993,787 | |
Less: Initial investment | $ 5,050,000 | |
NPV | $ (56,213) | |
NPV is negative due to rounding off of price per unit for 0 NPV. |