Managerial Accounting — Capital Budgeting: After-Tax Cash Flows, NPV, IRR and Payback

The short-term decisions of chapter 2 ignored the time value of money. For investments whose effects span several years — equipment, plants, new products — when cash comes in and goes out is decisive. Capital budgeting evaluates long-term investment proposals with cash flows and discounting. Estimating the discount rate (cost of capital) belongs to the corporate finance course.

1. Principles of incremental cash flows

• Cash flows: use cash flows, not accounting profit. Depreciation is not a cash outflow.
• Incremental: include only cash flows that change if the investment is made. Leave out sunk costs; include opportunity costs.
• After tax: reflect income tax. Depreciation involves no cash outflow, but it reduces taxable income and saves tax — the tax shield.
• Exclude interest: financing costs are already reflected in the discount rate, so they are not deducted from cash flows.
• Working capital: the increase in inventory and receivables at the start is a cash outflow, recovered when the project ends.

2. The project’s cash flows

Company BR plans to buy equipment for ₩10 million, with a five-year useful life, zero residual value and straight-line depreciation. Using it raises revenue by ₩6 million a year and cash operating costs by ₩2.5 million. It needs ₩1 million of working capital at the outset, recovered in full after five years. The tax rate is 20% and the discount rate 10%.

3. Evaluation methods

A. Net present value (NPV)

NPV is about ₩1.75 million, greater than zero, so the project is accepted. NPV shows in money terms how much the investment adds to firm value.

B. Internal rate of return (IRR)

IRR is the discount rate that makes NPV zero. NPV is about 22.4 at 15% and about −4.6 at 16% (₩10,000), so IRR is about 15.8%. IRR exceeds the 10% cost of capital, so the project is accepted.

C. Payback period and accounting rate of return

• Payback period: the time taken to recover the investment: $1{,}100 / 320 ≈ 3.44$ years. Easy to calculate and a signal of liquidity risk, but it ignores the time value of money and cash flows after payback.
• Accounting rate of return (ARR): average annual net income of $(350 - 200) \times 0.8 = 120$ (₩1.2 million) divided by the initial investment of ₩10 million is 12%. Easy to compute from accounting data, but it reflects neither cash flows nor the time value of money.

4. Conflicts between methods

If only one can be chosen, IRR picks A and NPV picks B. B adds more to firm value. IRR ignores scale and assumes intermediate cash flows are reinvested at the IRR. The rule is to choose between mutually exclusive projects on NPV. There is also the problem of multiple IRRs when the sign of cash flows changes more than once.

Check your understanding

Company BS can cut cash costs by ₩7 million a year by buying equipment for ₩20 million (four-year life, zero residual value, straight-line). The tax rate is 25% and the discount rate 8% (four-year annuity factor 3.3121). What are the annual after-tax cash flow, NPV and payback period?

Depreciation is ₩5 million a year. The after-tax cash flow is $700 \times 0.75 + 500 \times 0.25 = 525 + 125 = 650$ (₩6.5 million). NPV is $650 \times 3.3121 - 2{,}000 ≈ 2{,}152.9 - 2{,}000 = 152.9$ (about ₩1.53 million). The payback period is $2{,}000 / 650 ≈ 3.08$ years. NPV is positive, so the project is accepted.

References

• Charles Horngren, Srikant Datar and Madhav Rajan, Cost Accounting: A Managerial Emphasis, ch. 21
• Richard Brealey, Stewart Myers and Franklin Allen, Principles of Corporate Finance, ch. 5–6
• Ray Garrison, Eric Noreen and Peter Brewer, Managerial Accounting, ch. 14