Capital Investments
Practice As You Learn
The most common method used to make a capital investment decision is the net present value method.
Always follow these 4) steps when you work a net present value method problem:
1) Determine the cash inflows and cash outflows related to the investment
2) Determine the discount rate and go to the net present tables and get the present value factor for $1 and the present value of an annuity factor for the time periods related to the cash inflows and outflows.
3) Set up the table format and multiply the cash inflow or outflow by the net present value factor to get the net present value of the cash inflow or outflow. Present value is what it costs or what you receive valued in today’s dollars.
4) Total the net present value. If the net present value is positive it means that the investment will give a return higher than the required return (the discount rate)
Practice Problem – Capital Investments
A company is considering the purchase of a new machine that will cost $100,000. The machine is expected to increase the quality of the product produced and allow for price increases giving $15,000 per year of additional cash flow from revenues. Using the machine will save $8,000 per year in direct labor costs. Maintenance on the machine is expected to cost $4,000 per year. The company will use the machine for 10 years and then sell it for $10,000. The company’s required rate of return (discount rate) is 10%.
A. Determine the net present value of investing in the machine.
B. Determine the internal rate of return
C. Determine the payback period
D. Determine the accounting rate of return
Answer
A. Follow the 4) steps given to compute net present value.
1) Determine the cash inflows and cash outflows related to the investment
Cash inflows:
Added annual revenues $ 15,000
Save annual direct labor $ 8,000
Salvage value $ 10,000
Cash Outflows:
Purchase machine $100,000
Maintenance, annual $ 4,000
2) Determine the discount rate and go to the net present tables and get the present value factor for $1 and present value of an annuity for the time periods related to the cash inflows and outflows.
PV of $ — 10 years at 10% 0.3855
PV of annuity — 10 years at 10% 6.1446
3) Set up the table and multiply the cash inflow or outflow by the net present value factor to get the net present value of the cash inflow or outflow.
| PV | Present | |||||
| Cash flow descr. | Years | Amount of cash | x | Factor | = | Value of CF |
| Purchase | 0 | ($100,000) | 1.0 | ($100,000) | ||
| Maintenance | 10 | ($4,000) | 6.1446 | ($24,578) | ||
| Added Revenues | 10 | $15,000 | 6.1446 | $92,169 | ||
| Save direct labor | 10 | $8,000 | 6.1446 | $49,157 | ||
| Salvage value | yr 10 | $10,000 | 0.3855 | $3,855 | ||
| 4) Total Net Present Value | $20,603 | |||||
Total Net present value does NOT mean the company will have $20,603 more cash flow. The actual percentage return can not be determined with this method. This method tells management if the return will meet or exceed the required rate of return. A positive net present value means that the internal rate of return is higher than the required rate of return of 10%.
B. Determine the internal rate of return
Use the given formula and plug in the numbers to compute the factor to use in the present value table to determine the internal rate of return.
| PV Factor = 5.26 | Investment required Net annual cash inflow |
$100,000 $19,000 |
| Additional cash flow from revenues Additional maintenance costs Additional labor savings Net annual cash flows |
$15,000 ($4,000) $ 8,000 $19,000 |
Go to the present value of an annuity table and go down to period 10.
Go across the table until you get as close as you can to 5.26
14% is 5.2161 which is the closest
The investment in the machine will give a return of approximately 14%
C. Determine the payback period
The payback period is computed using the same formula as internal rate of return, but the answer is how many years it takes to recover the investment (not a factor to be used)
| Payback in years = 5.26 | Investment required $100,000 Net annual cash inflow $19,000 |
It will take approximately 5 years and 3 months to get the $100,000 investment returned in cash.
This formula does not consider the time value of money.
After 5.26 years, the investment earns a 0% return.
All of the positive return is essentially earned after 5.26 years.
D. Determine the accounting annual rate of return
Annual net cash flows – Annual depreciation
Initial Investment
| $19,000 – $9,000 = .10 = 10% $100,000 |
Depreciation = Cost $100,000 – $10,000 salvage / 10 years = 9,000 year
Annual net cash flow is the same as above.
Tax Considerations – Practice Problem – Capital Investment
If your instructor teaches that you should consider the impact of tax on the decision, you should do the following:
1) Begin with the same cash flows you identified above.
Cash Inflows:
Added annual revenues $ 15,000
Save direct labor $ 8,000
Salvage value $ 10,000
Cash Outflows:
Purchase machine $100,000
Maintenance $ 4,000
Convert the annual cashflows to after tax cashflows using a 30% tax rate
Revenues $15,000 x 70% = $10,500
Direct Labor $ 8,000 x 70% = $ 5,600
Maintenance ($ 4,000) x 70% = ($ 2,800)
Depreciation ($ 9,000) x 30% = $ 2,700
Net after tax annual cash flows $16,000
Depreciation $9,000 x 70% = ($ 6,300)
Net after tax impact to income $ 9,700
Depreciation is a tax deduction that reduces the income tax paid. The cash savings is a positive cash flow
Use the after-tax cash flows and multiply by the same present value factors
Use the impact to income determined just above in place of annual cash flows
for other formulas.