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Better Mousetraps has developed a new trap. It can go into production for an initial investment...
Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6.3 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $519,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.20 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 10%. Use the MACRS depreciation schedule. Year: 0 1 2 3 4 5 6 Thereafter Sales (millions of traps) 0 0.5 0.6 0.7 0.7 0.5 0.2 0
a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)
b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)
Solutions
Expert Solution
Initial Investment cash flows = Cost of equipment + Investment in working capital
Cost of equipment = 6,130,000
Investment in Working Capital for year 0 = 10% x First year sales
= 10% x 2500000
= $250000
Initial Investment cash flows = 6,130,000 + 250,000
= 6,380,000
All costs & values that impact cash flow negatively are shown in negative values
Sales and variable costs are derived from units sold and the respective per unit revenue and variable costs
Depreciation = (Equipment cost ) / Life of equipment
Depreciation = 6,130,000/ 6 = $1021667
Tax is 35% on EBIT
Working Capital for year 0 = 250000. It is the difference of previous and current year. If Working capital is increasing, it will bring down cash flow, thus shown as negative
So year, Working Capital for year 1 (Sales of 2nd year X 10%) = 10% x 3000000 = $300,000
The investment in WC in year 1 = Year 1 WC - Year 0 WC = 300000 - 250000 = 50000. Because this will negatively impact cash flow, it is shown as negative. Like wise for subsequent years
In the year 6, equipment would be sold at $519000
Net Cash flows from sale of equipment = Cash Flows from sale of equipment - Taxes
Tax on sale of equipment = (Sales Price - Book Value) x Taxes
Since the equipment is completely depreciated at end of year 6, the Book Value = 0
(Book Value = Purchase Price - Accumulated dividends)
Tax on sale of equipment = (519000 - 0) x 35% = 181650
Net Cash flows from sale of equipment = 519000 - 181650 = 337350
Cost of Capital (Discount Rate) =10%
Cash Flow = (Net Income + Depreciation + Net working capital investments + Capital Expenditure + After tax Salvage Value ) *
*Sign of cash flows are important here. One which increases CF is positive, other which decreases Cf is negative
PV of cash flows = CFt/ (1+k)^t
where CFt is cash flow in year t, k = Cost of capital (WACC) & t is the year of Cash flow
NPV = Sum of PV of all future cash flows - Investment
A) NPV of the project is = (1542583/ (1+10%)^1 + 1789583 / (1+10%)^2 + 2086583 / (1+10%)^3 + 2186583 / (1+10%)^4 + 1742583 / (1+10%)^5 + 1188933/ (1+10%)^6) - 6,130,000
=
$1315619
|
Forecast for Better Mousetraps |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
Units Sold (A) |
500000 |
600000 |
700000 |
700000 |
500000 |
200000 |
|
|
Sales Price / Unit (B) |
5.00 |
5.00 |
5.00 |
5.00 |
5.00 |
5.00 |
|
|
Operation cost/ Unit (C |
1.20 |
1.20 |
1.20 |
1.20 |
1.20 |
1.20 |
|
|
Revenues (D = A x B) |
2500000 |
3000000 |
3500000 |
3500000 |
2500000 |
1000000 |
|
|
Variable costs (E = A x C) |
-600000 |
-720000 |
-840000 |
-840000 |
-600000 |
-240000 |
|
|
Other Costs (F) |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
Depreciation (G = (L/6) |
-1021667 |
-1021667 |
-1021667 |
-1021667 |
-1021667 |
-1021667 |
|
|
EBIT (H = D + E + F + G) |
878333 |
1258333 |
1638333 |
1638333 |
878333 |
-261667 |
|
|
Taxes @ 35% (I = H x 35%) |
-307417 |
-440417 |
-573417 |
-573417 |
-307417 |
91583 |
|
|
Net Income (J = H + I) |
570917 |
817917 |
1064917 |
1064917 |
570917 |
-170083 |
|
|
Depreciation (G) |
1021667 |
1021667 |
1021667 |
1021667 |
1021667 |
1021667 |
|
|
Net Working Capital Investments (K) |
-250000 |
-50000 |
-50000 |
0 |
100000 |
150000 |
|
|
Capital Expenditure in Plant & Mach(L) |
-6130000 |
||||||
|
Salvage Value of Equipment (M) |
519000 |
||||||
|
Tax on Salvage Value (N) |
-181650 |
||||||
|
Free Cash Flow (O = J+G+K+L+M + N) |
-6380000 |
1542583 |
1789583 |
2086583 |
2186583 |
1742583 |
1188933 |
|
Cost of Capital(Discount Rate) R |
10.00% |
||||||
|
PV Of Free Cash Flow |
-6380000 |
1402348 |
1478994 |
1567681 |
1493466 |
1082007 |
671122 |
|
NPV (Sum of PV of all CF) |
1315619 |
||||||
|
Working Capital (at 10% of next year sales) W |
250000 |
300000 |
350000 |
350000 |
250000 |
100000 |
B) Using MACRS depreciation rate
NPV = Sum of PV of all future cash flows - Investment
NPV of the project is = (1614100/ (1+10%)^1 + 2118560 / (1+10%)^2 + 2140936 / (1+10%)^3 + 2076162 / (1+10%)^4 + 1632162 / (1+10%)^5 + 954931/(1+10%)^6) - 6,130,000
= $1417280
The increase in NPV using a
5 year MACRs schedule = $1417280 - $1315619
= $101662
MACRS depreciation rate
|
Year |
MACRS Depreciation |
|
Year 1 |
20.00% |
|
Year 2 |
32.00% |
|
Year 3 |
19.20% |
|
Year 4 |
11.52% |
|
Year 5 |
11.52% |
|
Year 6 |
5.76% |
Depreciation = (Equipment cost ) X MACRS depreciation rate for the year
The cash flows would appear as below
|
Forecast for Better Mousetraps |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
Units Sold (A) |
500000 |
600000 |
700000 |
700000 |
500000 |
200000 |
|
|
Sales Price / Unit (B) |
5.00 |
5.00 |
5.00 |
5.00 |
5.00 |
5.00 |
|
|
Operation cost/ Unit (C |
1.20 |
1.20 |
1.20 |
1.20 |
1.20 |
1.20 |
|
|
Revenues (D = A x B) |
2500000 |
3000000 |
3500000 |
3500000 |
2500000 |
1000000 |
|
|
Variable costs (E = A x C) |
-600000 |
-720000 |
-840000 |
-840000 |
-600000 |
-240000 |
|
|
Other Costs (F) |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
Depreciation (G = (L x MACRS Rate) |
-1226000 |
-1961600 |
-1176960 |
-706176 |
-706176 |
-353088 |
|
|
EBIT (H = D + E + F + G) |
674000 |
318400 |
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