Question

Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $3,900 and sell its old washer for $1,200. The new washer will last for 6 years and save $1,100 a year in expenses. The opportunity cost of capital is 19%, and the firm’s tax rate is 21%.
a. If the firm uses straight-line depreciation over a 6-year life, what are the cash flows of the project in years 0 to 6? The new washer will have zero salvage value after 6 years, and the old washer is fully depreciated. (Negative amounts should be indicated by a minus sign.)
b. What is project NPV? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
c. What is NPV if the firm investment is entitled to immediate 100% bonus depreciation? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

Cashflow

Yearo zero ($2,700)

from 1st to 6th: +$1,005.5

Net Present Value: $728.53

If bonus depreciation then:

Net Present Value:  $916.04

Explanation:

Cash Flow

Year zero:

-3,900 purchase of new machine

+ 1,200 sale from old machine

 -2,700

Years 1 through 6:

1,100 savings x (1 - 21% tax rate) = 869.0

depreciation

3,900 / 6 = 650

tax-shield on depreciation: 650 x 21% = 136.5

total cash-flow:

869 cost savings + 136.5 lesser taxes = 1005.5

We now solve for the Net present value we discount the cashflow at 19% which is the cost of capital and compare agaisn the year zero outflow:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 1,005.50

time 6

rate 0.19

$1005.5 \times \frac{1-(1+0.19)^{-6} }{0.19} = PV$

PV $3,428.5310

- $2,700 + $3,428.53 = $728.53

If bonus depreciation scenario:

at year 1 the entire equipment is depreciate

giving a tax shield of:

3,700 x 21%= 777

This will be discounted one year as the depreciation bonus which lowers taxes occurs at year-end:

777 / 1.19 = 652.94117647

Then, we solve for the present value of the cost savings only as the depreciations do not occur:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 869.00

time 6

rate 0.19

$869 \times \frac{1-(1+0.19)^{-6} }{0.19} = PV$

PV $2,963.0964

So we have:

-  2,700      year zero cash outflow

+    652.94 present value of bonus depreciation

+ 2,963.10 present value of the cost savings

     916.04 net present value