Better Mousetraps has developed a new trap. It can go into production for an ini
ID: 2820021 • Letter: B
Question
Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $54 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 $527,000. 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 $1.10 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm's tax bracket is 35%, and the required rate of return on the project is 9% Year: Oill 1: 12:111311 All SII/6 . Thereafter Sales (millions of 0 0.5 0.7 0.9 0.9 0.6 0. traps) Suppose the firm can cut its requirements for working capital in half by using better inventory control systems. By how much will this increase project NPV? (Enter your answer in millions rounded to 4 decimal places.) ange in NPV millionExplanation / Answer
In this case we need to calculate the change in NPV due to changes in the working capital if it's reduced to half by using better inventory control systems. For this, we need to understand the impact of working capital in calculating NPV. Working capital is a cash outflow when it's required and when the project is completed, the working capital is released and is then treated as a cash inflow. As working capital in this case is estimated to be 10% of next year's forecasted sales, the estimated is provided as per below:
If working capital requirement is the same amount each year, we need not have that cash outflow in each year. Outflows in the upcoming years will only be the incremental amount required.
Year
Sales (in Mn units)
Sales ($ Mn) (no. of units * price)
Working capital ($ Mn)@ 10% of next year
Working Capital Flows ($ Mn)
0
0
0
0.25
-0.25
1
0.5
2.5
0.35
-0.1
2
0.7
3.5
0.45
-0.1
3
0.9
4.5
0.45
0
4
0.9
4.5
0.3
0.15
5
0.6
3
0.2
0.1
6
0.4
2
0.2
Cash Inflows are the Sales, Tax saving from Depreciation, Residual value of machinery and the inflow of working capital wherever applicable.
Tax saving from depreciation is the depreciation value * Tax rate = (Initial cost of machinery/Life) * 35%
= ($5.4 Mn / 6) * 35%
= $0.315 Mn
Year
Sales (in Mn units)
Sales ($ Mn) (no. of units * price)
Residual value ($ Mn)
Release of WC ($ Mn)
Dep saving ($ Mn)
Total Cash Inflows ($ Mn)
PV
0
0
0
0
0
0
0
0
1
0.5
2.500
0.000
0.000
0.315
2.815
2.582569
2
0.7
3.500
0.000
0.000
0.315
3.815
3.211009
3
0.9
4.500
0.000
0.000
0.315
4.815
3.718063
4
0.9
4.500
0.000
0.150
0.315
4.965
3.517331
5
0.6
3.000
0.000
0.100
0.315
3.415
2.219516
6
0.4
2.000
0.527
0.200
0.315
3.042
1.813845
Present Value of Cash Inflows
17.06233
Year
Sales (in Mn units)
Prod cost ($ Mn) (no. of units * cost)
Working Capital Required ($ Mn)
Initial Investment ($ Mn)
Total Cash Outflows ($ Mn)
PV
0
0
0.0000
0.2500
5.4000
5.6500
5.6500
1
0.5
0.5500
0.1000
0.0000
0.6500
0.596330275
2
0.7
0.7700
0.1000
0.0000
0.8700
0.732261594
3
0.9
0.9900
0.0000
0.0000
0.9900
0.764461645
4
0.9
0.9900
0.0000
0.0000
0.9900
0.701340959
5
0.6
0.6600
0.0000
0.0000
0.6600
0.428954715
6
0.4
0.4400
0.0000
0.0000
0.4400
0.262357624
Present Value of Cash Outflows
9.135706812
NPV before improvement in Inventory Controls = (17.06233 – 9.1357) $ Mn
= $ 7.9266 Mn
After improvement in Inventory Controls, below will be the Working Capital requirement:
Year
Sales (in Mn units)
Sales ($ Mn) (no. of units * price)
Working capital ($ Mn)@ 5% of next year
Working Capital Flows ($ Mn)
0
0
0
0.125
-0.125
1
0.5
2.5
0.175
-0.05
2
0.7
3.5
0.225
-0.05
3
0.9
4.5
0.225
0
4
0.9
4.5
0.15
0.075
5
0.6
3
0.1
0.05
6
0.4
2
0.1
Based on the above, below are the new PV of Inflows calculation and PV of outflows calculation:
Year
Sales (in Mn units)
Sales ($ Mn) (no. of units * price)
Residual value ($ Mn)
Release of WC ($ Mn)
Dep saving ($ Mn)
Total Cash Inflows ($ Mn)
PV
0
0
0
0
0
0
0
0
1
0.5
2.500
0.000
0.000
0.315
2.815
2.582569
2
0.7
3.500
0.000
0.000
0.315
3.815
3.211009
3
0.9
4.500
0.000
0.000
0.315
4.815
3.718063
4
0.9
4.500
0.000
0.075
0.315
4.89
3.464199
5
0.6
3.000
0.000
0.050
0.315
3.365
2.187019
6
0.4
2.000
0.527
0.100
0.315
2.942
1.754218
Present Value of Cash Inflows
16.91708
Year
Sales (in Mn units)
Prod cost ($ Mn) (no. of units * cost)
Working Capital Required ($ Mn)
Initial Investment ($ Mn)
Total Cash Outflows ($ Mn)
PV
0
0
0.0000
0.1250
5.4000
5.5250
5.5250
1
0.5
0.5500
0.0500
0.0000
0.6000
0.550458716
2
0.7
0.7700
0.0500
0.0000
0.8200
0.690177594
3
0.9
0.9900
0.0000
0.0000
0.9900
0.764461645
4
0.9
0.9900
0.0000
0.0000
0.9900
0.701340959
5
0.6
0.6600
0.0000
0.0000
0.6600
0.428954715
6
0.4
0.4400
0.0000
0.0000
0.4400
0.262357624
Present Value of Cash Outflows
8.922751253
NPV = (16.9171 – 8.9228) $ Mn
= $ 7.9943 Mn
Our NPV is thus expected to increase by $ 0.0677 Mn.
Year
Sales (in Mn units)
Sales ($ Mn) (no. of units * price)
Working capital ($ Mn)@ 10% of next year
Working Capital Flows ($ Mn)
0
0
0
0.25
-0.25
1
0.5
2.5
0.35
-0.1
2
0.7
3.5
0.45
-0.1
3
0.9
4.5
0.45
0
4
0.9
4.5
0.3
0.15
5
0.6
3
0.2
0.1
6
0.4
2
0.2
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