Question

Unless stated otherwise, interest is compounded annually, and payments occur at the end of the period. Face value for bonds is $1000.

1. Saucer Inc. is interested in developing a new dish. The sales will be $250 million per year for 4 years. Operating costs are $210 million per year for 4 years. The project requires an additional machine that costs $120,000,000 to be depreciated to a zero book value on a straight‑line basis over 4 years. The project will generate $3,000,000 per year in interest expense. The net operating working capital needed per year is equal to 2% of the next year’s sales, and any remaining net operating working capital is returned at the end of year 4. Operating costs do not include depreciation and interest expenses. The cost of capital is 7% and the tax rate is 25%. The project ends at year 4. There is no horizon value.
   1. Find the net present value and internal rate of return.
   2. Should they develop the new dish?   Explain.   

Answer 1

Year 0 Year 1 Year 2 Year 3 Year 4 NPV Initial Investment Investment in working capital Operating Cash flow after tax Net Operating Cash flows Discount Factor @ 7% Discounted Cash flows (120,000,000) (5,000,000) 5,000,000 37,500,000 37,500,000 37,500,000 37,500,000 (125,000,000) 37,500,000 37,500,000 37,500,000 42,500,000 1 0.93457944 0.87343873 0.81629788 0.76289521 (125,000,000) 35,046,728.97 32,753,952.31 30,611,170.38 32,423,046.51 5,834,898.18

NPV is the Difference of Discounted Cash inflows and Discounted Cash outflows.

Working:

Depreciation Cost of Asset 120,000,000 4. Useful life Depreciation 30,000,000 Operating Cash flow after tax Sales 250,000,000 Less: Operating Costs Less: Depreciation Cash flow before tax Tax @25% Cash flow after tax Add Back Depreciation Operating Cash flow 210,000,000 30,000,000 10,000,000 2,500,000 7,500,000 30,000,000 37,500,000 Net Working Capital Sales 250,000,000 2% of Sales 5,000,000

IRR.

Cash inflows Cash inflows Discount Factor Discount discounted at discounted at Cash Inflows Year Factor @ 10% @7% 7% 10% 1 37,500,000.00 2 37,500,000.00 3 37,500,000.00 4 42,500,000.00 0.9346 35,046,728.97 0.909090909 34,090,909.09 0.8734 32,753,952.31 0.826446281 30,991,735.54 0.8163 30,611,170.38 0.751314801 28,174,305.03 29,028,071.85 0.7629 32,423,046.51 0.683013455 130,834,898.18 122,285,021.51

$IRR=7 + \frac{ 130,834,898.18 - 125,000,000}{ 130,834,898.18 - 122,285,021.51 }*( 10-7)$

$\therefore IRR = 9.05$

IRR = 9.05%

Formula for discount factor:

$Discount ~Factor = \frac{1}{(1+i)^n}$

Where, i = rate of discounting

n = number of periods.

Conclusion:

a. We got Net present value as  $5,834,898.18 and IRR as 9.05%

b. IRR (9.05%) is greater than required rate of return i.e 7%. This means that the required rate is 7% but the new project is giving 9.05%. Therefore, the new project must be accepted.