Chapter 11 - - The Basics of Capital Budgeting
I.Project Classifications
A.Replacement projects = expenditures to replace worn-out or damaged equipment required in the production of profitable products
B.Replacement: cost reduction = expenditures to replace serviceable but obsolete equipment and lower costs
C.Expansion of existing products or markets = expenditures to increase output of existing products or to expand retail outlets or distribution facilities in markets now being served
D.Expansion of new products or markets = expenditures to produce new products or to expand into new markets
E.Safety and/or environmental products = expenditures necessary to comply with government orders, labor agreements, or insurance policy terms
F.Other = expenditures on office buildings, parking lots, and executive aircraft
II.Capital Budgeting Techniques
A.Three ways to determine appropriate project, be it either an expansion or replacement project, independent projects or mutually exclusive projects
1.Payback period
2.Net present value (NPV)
3.Internal rate of return (IRR)
4.Modified internal rate of return (MIRR)
B.Example: After-tax, incremental cash flows of two projects
Year / Project A / Project B0 / -$42,000 / -$45,000
1 / 14,000 / 28,000
2 / 14,000 / 12,000
3 / 14,000 / 10,000
4 / 14,000 / 10,000
5 / 14,000 / 10,000
C.Payback period
1.Def’n: amount of time required for a firm to recover its initial investment in a project, as calculated from cash flows
Payback period = number of years prior to full recovery + (unrecovered cost at start of last year)/(cash flow during full recovery year)
2.Viewed as unsophisticated capital budgeting technique
3.Decision rule: Let N* years = firm’s maximum acceptable payback period
a.Independent projects: Accept all projects whose payback periods < N*
b.Mutually exclusive projects: Among those projects whose payback periods are < N*, choose the project with the shortest payback period
4.The example:
a.Project A: The cash inflow of every year = $14,000.
$42,000/14,000= 3 = => Project A’s payback period is 3 years
Year / 0 / 1 / 2 / 3 / 4 / 5Cash flow / -$42,000 / $14,000 / $14,000 / $14,000 / $14,000 / $14,000
Cumulative cash flow / -$42,000 / -$28,000 / -$14,000 / $0 / $14,000 / $28,000
Payback period = 3 years
b.Project B: To get $45,000 = => Need all the $28,000 of the 1st year ($17,000 left to go), need all the $12,000 of the second year ($5,000 left to go), need only $5,000 of the $10,000 earned during third year. To prorate the time need after the second year : $5,000/$10,000 = .5 year = => Project B’s payback period = 2.5 years
Year / 0 / 1 / 2 / 3 / 4 / 5Cash flow / -$45,000 / $28,000 / $12,000 / $10,000 / $10,000 / $10,000
Cumulative cash flow / -$45,000 / -$17,000 / -$5,000 / $5,000 / $14,000 / $28,000
Payback period = 2 years + $5,000/$10,000 years = 2.5 years
c.Let N* = 3.5 years
d.If independent projects: accept both projects because 3 < 3.5 and 2.5 < 3.5
e.If projects mutually exclusive: pick project B as 2.5 < 3 < 3.5
5.Pros and cons of the payback method
a.The pros:
i.Widely used
ii.Computationally simple
iii.Intuitive appeal
iv.Since it measures how quick firm recovers initial investment, gives implicit consideration to time value of money
v.By picking projects with payback < N* = => approach is may reduce risk and payback period has some relation to risk exposure
b.The con:
a.N* a subjective predetermined measure
b.Payback period not linked to goal of shareholder wealth maximization
c.Approach doesn’t fully take the time value of money into account (cash flows aren’t discounted to present value)
d.Payback period approach ignores cash flows received after the payback period.
6.One possible modification: Discounted payback at 10% cost of capital
a.Length of time required for investment’s cash flows, discounted at the cost of capital to cover its cost
b.Project A:
Year / 0 / 1 / 2 / 3 / 4 / 5Cash flow / -$45,000 / $14,000 / $14,000 / $14,000 / $14,000 / $14,000
Discounted cash flow / -$45,000 / $12,727 / $11,570 / $10,518 / $9,562 / $8,693
Cumulative discounted cash flow / -$45,000 / -$32,273 / -$20,702 / -$10,184 / -$622 / $8,071
Payback period = 4 + 622/8693 = 4 + .07 = 4.07
c.Project B
Year / 0 / 1 / 2 / 3 / 4 / 5Cash flow / -$45,000 / $28,000 / $12,000 / $10,000 / $10,000 / $10,000
Discounted cash flow / -$45,000 / $25,455 / $9,917 / $7,513 / $6,830 / $6,209
Cumulative discounted cash flow / -$45,000 / -$19,545 / -$9,628 / -$2,115 / $4,715 / $10,924
Payback period = 3 + 2115/6830 = 3 + 0.31 = 3.031
d.If N* = 4:
i.If projects are independent: Accept Project B and reject project A. 3.031 < 4 < 4.07
ii.If projects are mutually exclusive: Accept Project B and reject project A. 3.031 < 4 < 4.07
D.Net present value (NPV)
1.Def’n: sophisticated capital budgeting technique found by subtracting project’s initial investment from present value of future cash flows (which where discounted at rate equal to firm’s cost of capital)
2.Let CFt be the firm’s cash flow in year t. Let k be the firm’s cost of capital.
3.r = discount rate = required return = cost of capital = opportunity cost = minimum return that must be earned on project to leave firm’s market value unchanged
4.Decision rule:
a.Independent projects: Accept all projects with NPV > 0
b.Mutually exclusive projects: choose project with largest positive NPV
5.The example: Let r = 10%
a.Excel formula: NPV(discount rate, CF1, . . . , CFN) – CF0
b.Project A:
c.Project B
d.Decision rule:
i.If A and B are independent projects: pick both projects. $11,091 > 0 and $10,024 > 0
ii.If Projects A and B are mutually exclusive: Pick project A because $11,091 > $10,924 > 0
E.Internal Rate of Return (IRR)
1.Def’n: Sophisticated capital budgeting technique. It is that discount rate where the net present value of the project is equal to zero. It is the discount rate that equates the present value of the future cash flows with the initial investment.
2.Let IRR = the internal rate of return. IRR is the discount rate that solves the following equation:
3.Decision rule: let r = the firm’s cost of capital
a.Independent projects: Accept any project whose IRR > r.
b.Mutually exclusive projects: Among those projects with an IRR > r, choose the project with the largest IRR.
4.Excel formula: IRR(beginning cell:last cell, guess)
Enter yearly cash flows in order from initial investment to terminal cash flow. The beginning cell of the array contains the initial investment, while the last cell contains cash flows of the last year of the project. Guess is a fraction to initiate the convergence to the solution.
5.Example:
a.Project A - - IRR = 19.86%
b.Project B - - IRR = 21.65%
c.Decision rules: Let r = 10%
i.Independent projects: Since IRRA = 19.86% > 10.00% and IRRB = 21.65% > 10.00% → accept both projects A and B
ii.Mutually exclusive projects: Pick project B because IRRB > IRRAr or 21.65% > 19.86% > 10.00%. In this case, there is a conflict in the choices recommended by NPV and IRR. According to NPV, project A should be accepted, while according to IRR, project B is preferred.
III.The possibilities of conflicting rankings using NPV and IRR
A.Examine the net present value profiles
1.Net present value profile = graph depicting project’s NPV for various discount rates
2.Figure 1 is the NPV profiles for the example
Figure 1
3.Conflicting decisions: Independent vs mutually exclusive projects
a.Refer to figure : IRRA = k4 , IRRB = k6
Cross over rate where NPVA = NPVB = k2
b.Refer to Figure 2 on next page. Assume projects A and B are independent.
Cost of Capital / NPV Approach / IRR Approach / NPV and IRR Agree?k1 / Accept A; Accept B / Accept A; Accept B / Yes
k2 / Accept A; Accept B / Accept A; Accept B / Yes
k3 / Accept A; Accept B / Accept A; Accept B / Yes
k4 / Reject A; Accept B / Reject A; Accept B / Yes
k5 / Reject A; Accept B / Reject A; Accept B / Yes
k6 / Reject A; Reject B / Reject A; Reject B / Yes
k7 / Reject A; Reject B / Reject A; Reject B / Yes
Conclude: When projects are independent, NPV and IRR approach always agree.
c.Refer to Figure 2 on next page. Now assume projects A and B are mutually exclusive.
Cost of Capital / NPV Approach / IRR Approach / NPV and IRR Agree?k1 / Accept A; Reject B / Reject A; Accept B / No
k2 / Accept either A or B / Reject A; Accept B / No
k3 / Reject A; Accept B / Reject A; Accept B / Yes
k4 / Reject A; Accept B / Reject A; Accept B / Yes
k5 / Reject A; Accept B / Reject A; Accept B / Yes
k6 / Reject A; Reject B / Reject A; Reject B / Yes
k7 / Reject A; Reject B / Reject A; Reject B / Yes
Conclude: For mutually exclusive projects, if k < the crossover rate, then the recommendations of the NPV and IRR approaches will disagree. If k > the crossover rate then the recommendations of the two approaches agree.
Figure 2
d.Which approach is better?
i.NPV approach is theoretically correct. The NPV approach assumes cash flows are reinvested at the firm’s cost of capital. However, the IRR assumes the firm’s cash flows are reinvested at the IRR which is greater than the firm’s cost of capital. Because the cost of capital is a more realistic estimate of the rate at which the firm could reinvest intermediate cash flows, use of the NPV is theoretically preferable with its more conservative and realistic reinvestment rate of the cost of capital.
ii.Surveys show financial managers prefer IRR. Managers tend to talk more about rates of return than actual dollar returns. Managers comfortable with return data, they express interest rates and profitability in percentage rates. NPV seems less intuitive as it doesn’t measure benefits relative to amount invested.
B.Multiple IRR
1.Normal cash flows
a.A project has normal cash flows if it has one or more outflows (costs) followed by a series of cash inflows
b.Examples:
i.- + + + + +
ii.- - - + + + + +
2.Nonnormal cash flows
a.A project has nonnormal cash flows if a cash outflow occurs sometime after the inflows have commenced.
b.Examples:
i.- + + + + -
ii.- + + + - + + +
3.Key result: If a project has nonnormal cash flows, it can have multiple IRRs.
a.A project has nonnormal cash flows if a cash outflow occurs sometime after the inflows have commenced.
b.Example: Assume r = 12%
Year / 0 / 1 / 2Cash flow / -$400,000 / $960,000 / -$572,000
Discounted cash flow (r=12%) / -$400,000 / $857,143 / -$455,995
Cumulative discounted cash flow / -$400,000 / $457,143 / $1,148
i.PV = $1,148 → Accept project
ii.Find IRR. Solve following equation
400(1+IRR)2 -960(1+IRR)+572=0
400[IRR2 + 2(IRR) + 1] -960(1 + IRR) + 572 = 0
400(IRR2)-160(IRR)+12 =0
100(IRR2)-40IRR+3 = 0 →
Find two IRR: 10% and 30%
iii.See Table 1 and Figure 3 on next page
Table 1r / PV
0.00 / -$12,000.00
0.02 / -$8,612.07
0.04 / -$5,769.23
0.06 / -$3,417.59
0.08 / -$1,508.92
0.10 / $0.00
0.12 / $1,147.96
0.14 / $1,969.84
0.16 / $2,497.03
0.18 / $2,757.83
0.20 / $2,777.78
0.22 / $2,579.95
0.24 / $2,185.22
0.26 / $1,612.50
0.28 / $878.91
0.30 / $0.00
0.32 / -$1,010.10
0.34 / -$2,138.56
0.36 / -$3,373.70
0.38 / -$4,704.89
0.40 / -$6,122.45
0.42 / -$7,617.54
0.44 / -$9,182.10
0.46 / -$10,808.78
0.48 / -$12,490.87
0.50 / -$14,222.22
0.52 / -$15,997.23
0.54 / -$17,810.76
0.56 / -$19,658.12
Figure 1
C.Modified internal rate of return = MIRR
1.MIRR = discount rate at which the present value of a project’s cost is equal to the present of its terminal value, where the terminal value is found as the sum of the future values of the cash inflows, compounded at the firm’s cost of capital
2.Notation
a.COFt = cash outflow in year t
b.CIFt = cash inflow in year t
c.MIRR = modified internal rate of return
d.MIRR equates present value of terminal value to present value of costs
terminal value = TV =
PV cost =
MIRR is that interest rate that solves the following equation:
e.Decision rule: Accept project if MIRR > cost of capital = r
f.Example: Return to previous example of Projects A and B
Year / Project A / Project B0 / -$42,000 / -$45,000
1 / 14,000 / 28,000
2 / 14,000 / 12,000
3 / 14,000 / 10,000
4 / 14,000 / 10,000
5 / 14,000 / 10,000
i.Project A
PV of costs = $42,000
→ 15.27%
ii.Project B
PV of costs = $45,000
→ 14.89%
iii.Decision: If projects are independent → Accept both since MIRR > r
4.Note
a.MIRR solves multiple IRR problem, can never be more than one MIRR. Compare it to cost of capital.
b.Is MIRR good for choosing between mutually exclusive projects?
i.In general, no.
ii.Conflicts may occur if projects differ in length → In this case use NPV
Chapter 11: The Basics of Capital Budgeting. Page 1