Mom's Cookies Inc.is considering the purchase of a new cookie oven.The original cost of the old oven was $30,000; it is now 5 years old, and it has a current market value of $13,333.33.The old oven is being depreciated over a 10-year life towards a zero estimated salvage value on a straight line basis, resulting in a current book value of $15,000 and an annual depreciation expense of $3,000.The old oven can be used for 6 more years but has no market value after its depreciable life is over.Management is contemplating the purchase of a new oven whose cost is $25,000 and whose estimated salvage value is zero.Expected before-tax cash savings from the new oven
Are $4,000 a year over its full MACRS depreciable life.Depreciation is computed using MACRS over a 5-year life, and the required rate of return is 10 percent.Assume a 40 percent tax rate.What is the net present value of the new oven?

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV) of the new oven, we need to calculate the present value (PV) of the cash savings and the PV of the initial cost of the oven. Then, we subtract the PV of the initial cost from the PV of the cash savings to get the NPV.

PV of Cash Savings:
Since the cash savings are $4,000 per year before taxes and the tax rate is 40%, the after-tax cash savings will be $2,400 per year ($4,000 x (1-0.4)).
Using MACRS over a 5-year life, the depreciation schedule is:
Year 1: 20%
Year 2: 32%
Year 3: 19.2%
Year 4: 11.52%
Year 5: 11.52%
Year 6: 5.76% (assuming the oven has no salvage value)
We can use these percentages to calculate the annual depreciation expense for each year and the ending book value of the oven after each year. The table below shows the calculations:

| Year | Depreciation | Before-Tax Cash Savings | After-Tax Cash Savings |
|------|-------------|------------------------|------------------------|
| 1    | $5,000      | $4,000                 | $2,400                 |
| 2    | $8,000      | $4,000                 | $2,400                 |
| 3    | $4,800      | $4,000                 | $2,400                 |
| 4    | $2,880      | $4,000                 | $2,400                 |
| 5    | $2,880      | $4,000                 | $2,400                 |
| 6    | $1,440      | $4,000                 | $2,400                 |

To calculate the PV of the after-tax cash savings, we need to discount each year's cash savings by the required rate of return (10%) and sum them up. Using a financial calculator or Excel, we get a PV of $10,387.44.

PV of Initial Cost:
The initial cost of the new oven is $25,000. We can use the MACRS depreciation schedule to calculate the annual depreciation expense for each year and the ending book value of the oven after each year. The table below shows the calculations:

| Year | Depreciation | Book Value |
|------|-------------|------------|
| 1    | $5,000      | $20,000    |
| 2    | $8,000      | $12,000    |
| 3    | $4,800      | $7,200     |
| 4    | $2,880      | $4,320     |
| 5    | $2,880      | $1,440     |

To calculate the PV of the initial cost, we need to discount each year's book value by the required rate of return (10%) and sum them up. Using a financial calculator or Excel, we get a PV of $15,037.95.

NPV:
To get the NPV, we subtract the PV of the initial cost from the PV of the after-tax cash savings. $10,387.44 - $15,037.95 = -$4,650.51. However, since the NPV is negative, we reject the project.