Formula for the Net Investment Cost of asset Purchase price Delivery cost Installation cost Incremental working capital Immediate cost savings Proceed from sale of an asset Taxes on sale of old asset – asset – gain gain or taxes on sale sale of old asset – asset – loss loss Net Investment Incremental Cash Returns Increase in revenues Increase in cash charges Increase in depreciation Incremental cash returns
xxx xxx xxx
xxx xxx (xxx) (xxx) xxx (xxx) xxx
xxx xxx xxx xxx
Example The following data are given on a new machine and an old one that is intended to be replaced:
Cost (life – (life – 5 5 years) Book value (remaining life – life – 5 5 years) Market value Working capital requirement Annual revenue Annual out-of-pocket operating costs Immediate repairs on old machine to Operate efficiently Income tax rate
New P150,000
Old P
50,000
60,000 48,000 20,000
200,000 100,000
100,000 80,000 10,000
35.0%
Required: Compute for the Net investment and incremental cash returns. Net investment Cash outflow: Cost of new machine Incremental working capital Cash inflow and savings Net proceeds from sale of old Machine – Machine – Market Market value Add: Tax benefit on loss (60,000 – (60,000 – 48,000) 48,000) x 35%
P150,000 30,000
P 48,000 4,200
P180,000
P 52,200 Savings – cost on immediate repairs needed on old machine, net of tax P10,000 x (1 – 35%) Net Investment
6,500
58,700 P121,300
Incremental cash returns
Incremental net income Increase in annual revenue (P200,000 – P100,000) Increase in out-of-pocket Operating costs (P100,000 - 80,000) Increase in depreciation charges 150,000 5 years
P
(20,000) (18,000)
60,000 5 years
Incremental income before income tax Incremental income tax (35%) Incremental net income Add: Incremental depreciation Incremental cash returns
100,000
P P P
62,000
(21,700) 40,300 18,000 58,300
After getting the incremental cash return, the different capital budgeting me thods may now be applied. For the purpose of illustration, let us use the NPV to determine the acceptability of the project. Let us assume further that the cost of capital is 12 %.
NPV
-n
=
incremental cash return 1 - ( 1 + i ) i
=
58,300 1 – (1.12) 0.12
=
58,300 (3.6048) – 121,300
=
P88,859.84
-5
- net investment
- P121,300
Since the NPV is positive P88,859.84, then accept the project.
Capital Budgeting Decision on Projects With Unequal Lives
Decision making on projects that is independent with each other is a not so complex problem to deal with. Decisions can be made independently as long as the project meets the demand of the
firm regardless of their respective lives. However, if a project is mutually exclusive and it has unequal lives, the impact of different lives must be considered over comparable periods. The approaches are as follows: 1. Replacement Chain (Common Life) Approach 2. Equivalent Annual Annuity Approach
Replacement Chain (common life) Approach
It is a process where projects with unequal lives are compared to their respective NPVs with the assumption that at the end of the life of the project a replacement is made until the project proposal arrives at a common terminal date. The same amount of initial investment, cash inflows, cost of capital and life of the project are used. In replacement chain approach, the NPV is determined for each proposal, and one or more iterations can be completed to create comparable time frames for the proposals. Thus, the short-lived project proposal is reinvested at the required rate of return until it already equates to the longer-lived project proposal. By comparing the proposals over like-periods of time, accept-reject information for the various proposals becomes more reliable.
Example Cost of capital for both projects is 12% and it is mutually exclusive project. Project A 0 -40,000
1
2
3
8,000
14,000
13,000
2
3
13,000
12,000
4 12,000
5 11,000
6 10,000
NPV = P6,491
Project B 0 -20,000
1 7,000
-20,000 NPV = P5,155 3,669 P8,824
1
7,000 -3
NPV = P5,155 (1.12)
2
13,000
3
12,000
Based on the given example, project B has a life of 3 years while project A has 6 years. Since the two proposals have unequal lives and it is not proper to compare their NPVs based on the original life of B, it is assumed that project B is replaced with a similar investment at the end of 3 years. Thus, project B would be viewed as two project Bs. The first NPV of project B was P5,155 and upon replacement it created the second NPV of P3,669. The figure was obtained by getting the present value of the first NPV. Since the total NPV of project B is P8,824 and project A has P6,941, therefore project B should be accepted because of a higher NPV. Let say that the life of project A is 10 years and project B is 6 years, the replacement cycle for project A is 3 times and project B is 5 times being their least common denominator is 30.
Annualized Net Present Value (ANPV) Approach
The annualized Net Present Value (ANPV) method is used when comparing mutually exclusive projects that have unequal duration. ANPV is an efficient method to convert NPVs of projects with unequal duration into an ANPV for each specific project, which can then be compared. ANPV is determined by dividing the NPV of each project over its life using the appropriate cost of capital. For those projects with negative NPV shall be disregarded and those projects with positive NPV shall be divided by the present value factor for an annuity at the given cost of capital and the project’s life in order to get the annualized NPV.. The project proposal with the highest ANPV shall be chosen.
Example Anna Pova Corporation has two mutually exclusive projects X and Y that it can invest in. Initial investments investments required for project X and Y are P150,000 and P200,000 respectively. The duration of project X is 4 years and of project Y is 3 years. The incremental cash return from project X are P50,000 and from project Y is P90,000. The cost of capital of Anna Pova Corporation is 9% and both projects have an average risk, which means that alteration for risk adjusted discount rate is not required. The 9 % for cost of capital should be used for both projects. What is the ANPV for projects X and Y?
Answer First, compute for the NPV of project X.
NPVX
=
incremental cash return
=
50,000 1 – (1.09) 0.09
-4
-n
1-(1+i) i - P150,000
- net investment
=
50,000 (3.2397) – 150,000
=
P11,985
After getting the NPV of project X, compute for the value of its ANPV. ANPVX
=
NPV -n 1-(1+i) i
=
P11,985 -4 1 – (1.09) 0.09
=
P3,699.42
For project Y, get also the NPV. NPVY =
incremental cash return
=
-n
1-(1+i) i -3
90,000 1 – (1.09) 0.09
- P200,000
=
90,000 (2.531) – 200,000
=
P27,790
After getting the NPV of project Y, get the ANPV. ANPVY
=
NPV -n 1-(1+i) i
=
P27,790 -3 1 – (1.09) 0.09
=
P10,979.85
- net investment
Since the ANPV of project Y is (P10,979.85) higher than that of project X (P3,699.42), project Y should be selected.
