January 21 2014

Unit 4 Notes: Capital Budgeting: Determining which investments a firm should undertake

Leonard Vun Corporate Finance, MBA emba, lecture notes, MNGT6321, npv, unsw 0

Corporate Finance lecture notes for the EMBA at UNSW.

Company adds value to a business through its capital budgeting or investment decisions.

When examining an investment proposal we are interested only in the marginal or incremental cash flows associated with the project.

Incremental net cash flow of an investment proposal: the difference between the firm’s cash flows if the investment project is undertaken and the firm’s cash flows if the investment project is not undertaken.

NPV = -Initial Investment + ${\rm C}\left(\frac{{\rm 1-}{{\rm (1+r)}}^{{\rm -}{\rm n}}}{{\rm r}}\right)+\frac{{\rm Salvage\ }}{{{\rm (1+r)}}^{{\rm n}}}$

Challenging Issues

Sunk Costs Defined at the time of doing the NPV calculation it is any cost that have already been expended or happened in the past.

Common examples:

Research and development cots already incurred
Market research already done
Feasibility studies performed
Machines purchased but not yet installed
Other cash outflows that can’t be recovered

Exam tip: Specify you are ignoring sunk costs

Calculating required rate of returns

Consider how firm’s assets are funded

Debt – use yield to maturity on firm’s bonds (interest rate for the debt);
Equity – use required return of shareholders (CAPM formula);
Calculate weight average of cost of debt and equity

Costs of raising debt and equity

Cost of finance is included in the discount rate of return (r)

Price Inflation

Be consistent on the NPV calculation. If Revenue and Expenses

Use current prices without inflation, use real discount rate. Real discount rate = Discount rate – inflation
Includes inflation, use discount rate

Projects tie up working capital

Cash outflow at time = 0
Cash inflows at the end of the project unless stated otherwise

Projects have different lengths

If mutually exclusive (alternatives cannot be repeated): Compare NPVs and choose the highest.
If alternative can be repeated then for each one:

Calculate NPV using standard method
Calculate the present value of $1 annuity over the life of the project
Adjusted NPV= ${\rm NPV}\left[\frac{{{\rm r}}_{{\rm p}}}{{{\rm (1-(1+}{{\rm r}}_{{\rm p}}{\rm )}}^{{\rm -n}}{\rm )}}\right]$
Choose alternative with highest “Adjusted NPV”

Payback period

Length of time to recover original investment;
Management establish maximum threshold
Rule:
Accept if payback period < desired recovery period;
Mutually exclusive investment, select investment with lowest payback period < desired recovery period

Pros	Cons
Simple answer in years	Ignores time value
Easy to explain	Ignores CFs after threshold
Can calculate in head	Problems with scale e.g. if one project has shorted payback period than the other project

Internal rate of return (IRR)

Find the discount rate which makes NPV = 0
Rules:
Accept if IRR > rate of return
Mutually exclusive investment, select the highest IRR above r_p

Pros	Cons
Simple answer in %	Problems with timing of cash flows. It does not take the ordering of inflows and outflows into account. In others it can’t distinguish between borrowing and lending.
Easy to explain	Multiple % answers. For each change of sign of successive cash flow through time E.g. clean up cost.
Decision often same as NPV	Problems with scale

Depreciation

It is not a cash flow – accounting tool for allocating cost of an asset as it is used up.

Need for NPV because it influences tax cash flow. It is tax deductible, the reduction in tax is a benefit and it is a cash flow.

First calculate deprecated value of asset
Depreciation =

Cost = purchase price + installation price + sales tax + delivery charges

Second calculate gain or loss on sale
Gain on sale = Disposal price – Book value > 0. It is taxable (-ve cash flow) in the period the sale takes effect
Loss on sale = Disposal price – Book value < 0. It is claimed as deduction (+ve cash flow ) in the period the sale takes effect

NPV Template

	0	1..n-1	Final year n
Annual Revenue (+)[=R]
Annual Expenses (-)[=E]
Investment Cash flow [=I] (initial cost (-ve) includes +sales, +deliver, +install);Salvage value (+ve)			+Salvage value (at end of life)
Changes in Working Capital (-)[=ΔWC = CA-CL]Add (+ve) WC back in at the end of project	-WC		+WC
Depreciation over the life of the asset (-) $[=D${}_{t}= (\frac{{\rm Asset\ cost}{\rm \ -\ Salvage\ price}}{{\rm useful\ life\ of\ asset}}))]$ Asset cost includes sales tax, delivery charges, setup install
Check for any gain or loss on sale.Book value = Original Cost – Depreciation x Years Gain (-ve) /Loss (+ve) on sale [=G_t] = Sold Price – Book Value
Tax cash flow (-)T_t = τ (R_t + E_t + D_t + G_t) x -1
After Tax cash flow[X_t=R_t – E_t – I_t – T_t]
Calculate PV of cash flow

WC is after-tax amount; do not include it when determining tax payable

Decision Criteria

Accept an investment if NPV > 0
Reject an investment if NPV < 0
Indifferent between accepting or rejecting an investment if NPV = 0
Accept the investment with the highest positive NPV if you must decide between mutually exclusive investments (i.e. must choose one, select A or Investment B)
Accept any investment if the investment have positive NPV between independent investments (can be A, B, both A and B or neither if negative NPV)
Accept the investment with the highest Annual Equivalent Cash Flow (AE) if you must decided between mutually exclusive investments with different life spans:

${\rm AE=NPV}\left[\frac{{{\rm r}}_{{\rm p}}}{{{\rm (1-(1+}{{\rm r}}_{{\rm p}}{\rm )}}^{{\rm -n}}{\rm )}}\right]$