課程三 :Investment Decision with Certainty 課程重點 : –Introduce MIRR –Identify the relevant cash flows –An example –Discussing capital rationing –Hoemwork assignment –Excel tools

Problems with IRR Multiple IRRs Mutually exclusive projects NPV method implicitly assumes that the rate at which cash flows can be reinvested is the cost of capital, whereas the IRR method implies that the firm has the opportunity to invest at the IRR.

Modified Internal Rate of Return (MIRR) The discount rate at which the present value of a project’s cost is equal to the present value 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. PV cost = PV terminal value The future value of the cash inflows is also called the terminal value.

MIRR example

Advantages of MIRR MIRR assumes that cash flows from all projects are reinvested at the cost of capital. MIRR also solves the multiple IRR problem. Mutually exclusive projects: –Equal size, same life:same decision as NPV –Equal size, different life: same –Different size: could have different decision as NPV

Identify the relevant cash flows Only cash flow is relevant. Not accounting income Estimating cash flows on an incremental basis. –Do not confuse average with incremental payoffs. –Include incidental effects. Externalities –Do not forget working capital requirements. –Forget sunk costs. –Include opportunity costs. –Be ware of allocated overhead costs. Be consistent in your treatment of inflation.

An example

Payback period: 3.15 years. IRR: 21.9% versus a 12% cost of capital. MIRR:18.9 versus a 12% cost of capital. NPV:$6988

Effect of NWC on cash flow

An example for treating inflation Assuming 15% nominal rate, and inflation is 10%.

Two approaches Restate the cash flows in nominal terms and discount at the nominal rate. Restate the discount rate in real terms and use this to discount the real cash flows.

Comparing projects with unequal lives Replacement chain approach: assuming that each project can be repeated as many times as necessary to reach a common life span; the NPVs over this life span are then compared, and the project with the higher common life NPV is chosen.

Equivalent annual annuity (EAA) approach 1.Find each project’s NPV over its initial life. 2.There is a constant annuity cash flow that has the same present value as a project’s NPV. 3.The project with a higher EAA will always have a higher NPV when extended out to any common life.

Projects With Unequal Lives: Equivalent Annual Annuity Year A B C 0-$300,000-$1,000,000-$600, , , , , , , , , , , ,000 Find the value of an annuity that has the same life as each project: For Project A Solve the following for EAA: NPV= $468,590 EAA A x PVIFA 12%,3 = $468,590 you get EAA A = $195,100 For Project B Solve the following for EAA: NPV= $1,466,840 EAA B x PVIFA 12%,6 = $1,466,840 you get EAA B = $356,774 For Project C Solve the following for EAA: NPV= $752,040 EAA C x PVIFA 12%,2 = $752,040 you get EAA C = $444,968

Equivalent Annual Costs Same as Equivalent Annual Annuity Except with Costs Consider the Following Example: Assume machine A and B have cost payment schedule as follows, which machine we should buy. MachineC 0 C 1 C 2 C 3 NPV(6%) A$15 $4 $4 $4 $25.69 B$10 $6 $6 $21.00 Again the technique involves finding the value of an annuity that has the same life as each machine. For Project A: EAA A x PVIFA 6%,3 = $25.69 Equivalent Annuity Payment = $25.69/2.673 = $9.61 For Project B: EAA B x PVIFA 6%,2 = $21.00 Equivalent Annuity Payment = $21.00/1.833 = $11.45

Capital rationing Internal capital rationing(or soft rationing): Managers either limit arbitrarily the total amount invested or the kind of investments the firm undertakes or set acceptance criteria that lead it to reject some investments that are advantageous when judged by market criteria. External capital rationing(or hard rationing) There is a difference between that market rate or interest which the firm can borrow money and the market rate at which it can lend.

Ranking by Profitability Index If budget limit is $10, we should accept project B and C.

More constraints A $10 budget limit applied to cash flows in each of year 0 and 1, which project we should choose, B & C, or A & D.

Linear Programming Max 21 X A +16X B +12X C +13X D s.t. 10 X A +5X B +5X C +0X D  X A -5X B -5X C +40X D  10 0  X A  1 0  X B  1 0  X C  1 0  X D  1

First Homework Assignment Please use EXCEL to complete this assignment. Questions: 1. Using Payback Period Method,discounted payback period, NPV, IRR, PI to decide whether accept individual projects. 2. Under each evaluation method, ranking projects. Describe any observation. 3. Assuming project 7 and 8 are mutually exclusive projects, using MIRR, EAA method to evaluate those projects.