Question

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 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 $606,000. 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 $1.70 per trap and believes that the traps can be sold for $7 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 12%. Use the MACRS depreciation schedule. Year: 0 1 2 3 4 5 6 Thereafter Sales (millions of traps) 0 0.5 0.7 0.9 0.9 0.6 0.3 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.)

Answer 1

1. INITIAL INVESTMENT OF PROJECT = $5.4 MILLION

2.ASSETS IS DEPRECIATED OVER 6 YEAR LIFE

3.CALCULAION OF DEPRECIATION.

STRAIGHT LINE DEPRECIATION = INITIAL INVESTMENT - SCRAP VALUE/NUMBER OF YEAR

= $5.4 - $6.06/6

= $7.99 PER YEAR DEPRECIATION

CALCULATION OF NPV

PARTICULAR    0    1    2    3 4    5 6   

INITIAL INVESTMENT ($5.4)

REVENUE - $3.5    $4.9 $6.3    $6.3    $4.2    $2.1

- WORKING CAPITAL $ (.35) $(1.35) $(1.82) $(2.16) $(1.95) $(1.23)    $0

- PRODUCTION COST    -    $(.85)    $(1.19)    $ (1.53) $(1.53) $(1.02) $(.51)

PBT    ($5.75)    $1.3 $1.89 $2.61 $2.82    $1.95 $1.59

LESS DEPRECIATION    - $.799    $.799    $.799    $.799 $.799    $.799

PBT ATER DEP ($5.75) $.501    $1.091    $1.811    $2.021 $1.151 $.791

LESS TAX @35% -    $.17535 $.38185 $.63385    $.70735    $.40285 $.27685

PAT ($5.75)    $.32565    $.70915 $1.17715    $1.31365 $.74815    $.51415

ADD DEPTRECIATION - $.799 $.799    $.799 $.799 $.799    $.799

TOTAL    (A)    -    $1.12465 $1.50815    $1.97615    $2.11265 $1.54715 $1.31315

PV FACTOR@12% (B)    1 .893    .797    .712 .636 .567    .507

(A) * (B)    ($5.75) $1.0043 $1.2019 $1.4070    $1.3436    $.8772    $.6657

NET PRESENT VALUE

PRESENT VALUE OF CASH INFLOW = $6.4997

ADD SCRAP VALUE=.606*.452 = $.2739

TOTAL    = $6.7736

LESS = PV OF CASH OUTFLOW =-($5.75)

NET PRESENT VALUE =$1.0236

* WORKING CAPITAL CALCULATION

=NEXT YEAR FORECAST SALE = AS GIVEN IN QUESTION

= $.5 MILLION

THEREFORE = $.5 *7 = $3.5

WORKING CAPITAL 10% OF FORECAST SALE = 3.5*10% = $.35

*PRODUCTION COST

1.7 FIRST YEAR SALE VALUE IS 0 THEREFORE PRODUCTION COST IS NIL

SECOND YEAR SALE IS $.5*$1.7=$.85

CALCULATION OF PRESENT VALUE

1/1.12 FOR 6 YEARS

B.IF FIRM DEPRECIATED ASSETS 5 YEARS SCHEDULE THEN SOLUTION WILL BE AS FOLLOW

PARTICULAR    0    1    2    3 4    5 6   

INITIAL INVESTMENT ($5.4)

REVENUE - $3.5    $4.9 $6.3    $6.3    $4.2    $2.1

- WORKING CAPITAL $ (.35) $(1.35) $(1.82) $(2.16) $(1.95) $(1.23)    $0

- PRODUCTION COST    -    $(.85)    $(1.19)    $ (1.53) $(1.53) $(1.02) $(.51)

PBT    ($5.75)    $1.3 $1.89 $2.61 $2.82    $1.95 $1.59

LESS DEPRECIATION    -   $.9588 $.9588   $.9588    $.9588   $.9588 -

PBT ATER DEP ($5.75) $.3412 $.9312    $1.6512    $1.8612 $.9912    $1.59

LESS TAX @35% -    $.11942 $..32592 $.57792    $.65142    $.34692    $.5565

PAT ($5.75)    $.22178 $.60528 $1.07328    $1.20978 $.64428    $1.0335

ADD DEPTRECIATION -    $.9588 $.9588 $.9588   $.9588   $.9588 -

TOTAL    (A)    -    $1.18058 $1.56408    $2.03208    $2.16858 $1.60308 $1.0335

PV FACTOR@12% (B)    1 .893    .797    .712    .636 .567    .507

(A) * (B)    ($5.75) $1.0542 $1.2466 $1.4468 $1.3792 $.9089    $.5239

NET PRESENT VALUE

PRESENT VALUE OF CASH INFLOW $6.5596*10,00,000 = $6559600

ADD SCRAP VALUE=.606*.452 $.2739*10,00,000 = $273900

TOTAL    = $ 6833500

LESS = PV OF CASH OUTFLOW ($5.75)*10,00,000 = $5750000

NET PRESENT VALUE = $1083500