Problem 14-21 (continued)
3. Which ranking is best will depend on Revco Products’ opportunities for
reinvesting funds as they are released from the project. The internal
rate of return method assumes that any released funds are reinvested at
the internal rate of return. This means that funds released from project
#2 would have to be reinvested in another project yielding a rate of
return of 19%. Another project yielding such a high rate of return might
be difficult to find.
The profitability index approach assumes that funds released from a
project are reinvested in other projects at a rate of return equal to the
discount rate, which in this case is only 10%. On balance, the
profitability index is the most dependable method of ranking competing
Problem 14-22 (20 minutes)
1. The annual net cash inflows would be:
Reduction in annual operating costs:
Operating costs, present hand method …..
$30,000
Operating costs, new machine ……………..
7,000
Annual savings in operating costs …………
Increased annual contribution margin:
6,000 boxes × $1.50 per box……………….
Total annual net cash inflows …………………
$32,000
2. The net present value is computed as follows:
Now
1
2
4
5
Purchase of machine …….
$(120,000)
Annual net cash inflows .
$32,000
$32,000
$32,000
$32,000
Replacement parts ……….
Salvage value of machine
________
______
______
______
7,500
Total cash flows (a) ……..
$(120,000)
$32,000
$32,000
$32,000
$39,500
Discount factor (20%) (b)
Present value (a)×(b) …..
$(120,000)
$22,208
$13,317
$15,424
$15,879
Net present value ………..
Problem 14-23 (45 minutes)
1. The payback periods for Products A and B are calculated using a two–
step process. First, the annual net cash inflows are calculated as
follows:
Product A
Product B
Sales revenues …………………………...
$250,000
$350,000
Variable expenses ………………………..
(120,000)
(170,000)
Fixed out-of–pocket operating costs …
(70,000)
(50,000)
Annual net cash inflows ………………..
$ 60,000
$130,000
The second step is to compute each product’s payback period as
follows:
Product A
Product B
Investment required (a) ………………..
Annual net cash inflow (b) ……………..
$60,000
Payback period (a) ÷ (b) ……………….
Problem 14-23 (continued)
2. The net present values for Products A and B are computed as follows:
Product A:
Now
Years
1-5
Purchase of equipment …………..
$(170,000)
Sales ………………………………….
$250,000
Variable expenses ………………….
(120,000)
Fixed out-of–pocket costs ………..
(70,000)
Total cash flows (a) ……………….
$(170,000)
Discount factor (16%) (b) ……….
Present value (a)×(b) …………….
$(170,000)
$196,440
Net present value ………………….
Product B:
Now
Years
1-5
Purchase of equipment …………..
$(380,000)
Sales ………………………………….
$350,000
Variable expenses ………………….
(170,000)
Fixed out-of–pocket costs ………..
Total cash flows (a) ……………….
$(380,000)
Discount factor (b) ………………..
Present value (a)×(b) …………….
$(380,000)
Net present value ………………….
Problem 14-23 (continued)
3. The internal rate of return for each product is calculated as follows:
Product A
Product B
Investment required (a) ………………………..
$170,000
$380,000
Annual net cash inflow (b) …………………….
$60,000
$130,000
Factor of the internal rate of return (a) ÷ (b)
2.833
2.923
4. The profitability index for each product is computed as follows:
Product A
Product B
Present value of cash inflows (a) …………….
$196,440
$425,620
Investment required (b) ………………………..
$170,000
$380,000
Profitability index (a) ÷ (b)…………………….
1.16
1.12
5. The simple rate of return for each product is computed as follows:
Product A
Product B
Annual net cash inflow ………………………….
$60,000
$130,000
Depreciation expense …………………………...
Annual incremental net operating income ….
$26,000
Product A
Product B
Annual incremental net operating income (a)
$26,000
Initial investment (b) …………………………...
$170,000
$380,000
Simple rate of return (a) ÷ (b) ……………….
6. The net present value calculations suggest that Product B is preferable
to Product A. However, the profitability index reveals that Product A is
the preferred choice. The payback period, internal rate of return, and
simple rate of return all favor Product A over Product B. However, it
bears emphasizing that Lou Barlow may be inclined to reject both
products because the simple rate of return for each product is lower
Problem 14-24 (45 minutes)
1.
Present cost of transient workers ……………………..
$40,000
Less out–of-pocket costs to operate the cherry picker:
Annual savings in cash operating costs ………………
$21,000
2. The first step is to determine the annual incremental net operating
income:
Annual savings in cash operating costs ………….
$21,000
Less annual depreciation ($94,500 ÷ 12 years) .
Annual incremental net operating income ………
3. The formula for the payback period is:
Investment required
Payback period = Annual net cash inflow
Problem 14-24 (continued)
4. The formula for the internal rate of return is:
Investment required
Factor of the internal=
rate of return Annual net cash inflow
Problem 14-25 (30 minutes)
1. The present value of the purchase alternative is computed as follows:
Purchase Alternative:
Now
1
2
3
Purchase of cars ………
$(170,000)
Annual servicing costs .
$(3,000)
$(3,000)
$(3,000)
Repairs ………………….
(1,500)
(4,000)
(6,000)
Resale value of cars ….
________
______
______
Total cash flows (a) ….
$(170,000)
$(4,500)
$(7,000)
Discount factor (b) …..
Present value (a)×(b) .
$(170,000)
$(3,812)
$(5,026)
Net present value …….
$(132,554)
2. The present value of the lease alternative is computed as follows:
Lease Alternative:
Now
1
2
3
Security deposit ……….
$(10,000)
Annual lease payments
$(55,000)
$(55,000)
$(55,000)
Refund of deposit …….
_______
_______
_______
10,000
Total cash flows (a) ….
$(10,000)
$(55,000)
$(55,000)
$(45,000)
Discount factor (b) …..
Present value (a)×(b) .
$(10,000)
$(46,585)
$(39,490)
$(27,405)
Net present value …….
$(123,480)
3. The company should lease the cars because this alternative has the
lowest present value of total costs.
Problem 14-26 (30 minutes)
1. The annual incremental net operating income can be determined as
follows:
2. The simple rate of return is:
Annual incremental net operating income
Simple rate=
of return Initial investment (net of salvage from old equipment)
$40,500 $40,500
= = = 15%
$330,000 – $60,000 $270,000
Yes, the water slide would be constructed. Its return is greater than the
specified hurdle rate of 14%.
3. The payback period is:
Investment required (net of salvage from old equipment)
Payback =
period Annual net cash inflow
Problem 14-27 (30 minutes)
1. Average weekly use of the auto wash and the vacuum will be:
$1,350
Auto wash: = 675 uses
$2.00
Vacuum: 675 × 60% = 405 uses
The expected annual net cash receipts from operations would be:
Auto wash cash receipts ($1,350 × 52) ……….
$70,200
Vacuum cash receipts (405 × $1.00 × 52) ……
21,060
Total cash receipts ………………………………..
91,260
Less cash disbursements:
Water (675 × $0.20 × 52) ………………………
$ 7,020
Electricity (405 × $0.10 × 52) …………………
Rent ($1,700 × 12) ……………………………….
Cleaning ($450 × 12) …………………………….
Insurance ($75 × 12) …………………………….
Maintenance ($500 × 12) ……………………….
Total cash disbursements ………………………….
41,826
Annual net cash receipts from operations ……..
$49,434
Problem 14-27 (continued)
2. The net present value is computed as follows:
Now
Years
1-5
Year
5
Purchase of equipment …..
$(200,000)
Working capital …………….
(2,000)
Annual net cash flows …….
$49,434
Working capital released …
$2,000
10%) ………………………….
20,000
Total cash flows (a) ……….
$(202,000)
$49,434
Discount factor (b) ………..
0.621
Present value (a)×(b) …….
$(202,000)
Net present value ………….
Problem 14-28 (20 minutes)
1. The net present value of keeping the old truck is computed as follows:
Keep the old truck:
Now
Years
1-5
Year
5
Overhaul needed now ……
$(7,000)
Annual operating costs…..
(10,000)
Salvage value (old) ……….
_______
Total cash flows (a) ………
$(7,000)
$1,000
Discount factor (b) ……….
0.476
Present value (a)×(b) ……
$(7,000)
Net present value …………
2. The net present value of purchasing the new truck is computed as
follows:
Purchase the new truck:
Now
Years
1-5
Year
5
Purchase new truck ………
$(30,000)
Salvage value (old) ……….
9,000
Annual operating costs…..
(6,500)
Salvage value (new) ……..
_______
______
$4,000
Total cash flows (a) ………
$(21,000)
$(6,500)
$4,000
Discount factor (b) ……….
1.000
0.476
Present value (a)×(b) ……
$(21,000)
$1,904
Net present value …………
$(40,377)
3. The company should keep the old truck because the present value of
the net cash outflows is $1,113 lower for that alternative.
Problem 14-29 (45 minutes)
1. A net present value computation for each investment follows:
Common stock:
Now
Years
1-3
Year
3
Purchase of the stock .
$(95,000)
Sales of the stock …….
________
______
Total cash flows (a) ….
$(95,000)
Discount factor (b) …..
Net present value …….
Preferred stock:
Now
Years
1-3
Year
3
Purchase of the stock .
$(30,000)
Annual cash dividend
($30,000 × 0.06) ……..
$1,800
Sales of the stock …….
________
______
$27,000
Total cash flows (a) ….
$(30,000)
$1,800
$27,000
Discount factor (b) …..
1.000
2.246
0.641
Present value (a)×(b) .
$(30,000)
$4,043
$17,307
Net present value …….
$(8,650)
Bonds:
Now
Years
1-3
Year
3
Purchase of the bonds
$(50,000)
Annual interest income
$6,000
Sales of the bonds ……
________
______
$52,700
Total cash flows (a) ….
$(50,000)
$6,000
$52,700
Present value (a)×(b) .
$(50,000)
$13,476
$33,781
Net present value …….
$(2,743)
Problem 14-29 (continued)
2. Considering all three investments together, Linda did not earn a 16%
rate of return. The computation is:
Net
Present
3.
Investment required
Factor of the internal =
rate of return Annual net cash inflow
Substituting the $239,700 investment and the factor for 14% for 12
periods into this formula, we get:
=
$239,700 5.660
Annual cash inflow
Therefore, the required annual net cash inflow is: $239,700 ÷ 5.660 =
$42,350.
Problem 14-30 (60 minutes)
1. Computation of the annual net cost savings:
Savings in labor costs (25,000 hours × $16 per hour) ..
$400,000
Savings in inventory carrying costs …………………………
210,000
Total………………………………………………………………..
610,000
Less increased power and maintenance cost …………….
30,000
Annual net cost savings …………………………..…………..
$580,000
2. The net present value is computed as follows:
Now
1
2
3
4
5
Cost of the robot …..
$(1,600,000)
Installation &
software ……………..
(450,000)
Annual net cost
savings ……………….
$580,000
$580,000
$580,000
$580,000
$580,000
Inventory reduction .
Salvage value (old) ..
Total cash flows (a) .
$(2,050,000)
Discount factor (b) ..
Present value
Net present value ….
Problem 14-30 (continued)
3. Recomputation of the annual net cost savings:
Savings in labor costs (22,500 hours × $16 per hour)
$360,000
Savings in inventory carrying costs ………………………
210,000
Total……………………………………………………………..
570,000
Less increased power and maintenance cost ………….
30,000
Annual net cost savings …………………………..………..
$540,000
The revised present value computations are follows:
Now
1
2
3
4
5
Cost of the robot …..
$(1,600,000)
Installation &
software ……………..
(525,000)
Inventory reduction .
Salvage value (old) ..
Total cash flows (a) .
Discount factor (b) ..
Present value
Net present value ….
Problem 14-30 (continued)
4. a. Several intangible benefits are usually associated with investments in
automated equipment. These intangible benefits include:
◼ Greater throughput.
◼ Greater variety of products.
◼ Higher quality.
◼ Reduction in inventories.
The value of these benefits can equal or exceed any savings that may
come from reduced labor cost. However, these benefits are hard to
quantify.