3. Consider the following two mutually exclusive projects, X and Y, and their ca

Question

3. Consider the following two mutually exclusive projects, X and Y, and their cash flows information, Project Year 0 Year 1 Year 2 Year 3 Year 4 X ($1,400) $350 $750 $650 $650 Y ($1,000) $300 $400 $500 $600

(a) Assume that the discount rate is 12%, compute the payback period, the IRR, NPV and PI of project X.

(b) Use the McKinsey’s approach to compute the Modified IRR (MIRR) for project X.

(c) Apply the incremental IRR analysis to compute the crossover rate for projects X and Y, and select between these two mutually exclusive projects.

4. The following are two popular approaches used by automobile dealers:

(a) Cash Rebate Versus Low Rate Dealer Financing You are given two mutually exclusive options from the dealer on a $20,000 car:

(i) $1,500 cash rebate or

(ii) 36-month low rate loan at 3% APR. The prevailing APR on 36-month auto loan from a typical bank is 8%. Which option is a better deal?

(b) Buying Versus Leasing You are interested in a $25,000 car. A simplified leasing contract includes the following:

(i) up-front cost of $3,000, (ii) $400 monthly lease payment over a 36-month period, and

(iii) purchase cost of $12,000 at the end of the lease. What are the “implied” APR and EAR of the lease? Should you lease the car or buy and finance the car with a loan from the bank in (a)?

Explanation / Answer

3. (a).

NPV Calculation :

NPV = Net present value of all cash inflows -  Net present value of all cash outflows

Payback Period Calculation:

Positive Cumulative Present value of cash flow comes in the year 4. So Payback period is 3 years and time required to payback negative value of $26.9 in the year 4

So Payback period = 3 years + (26.9/413.1)*365 days = 3 years + 24 days i.e. 3years and 24 days

IRR Calculation:

Profitability index(PI) = Present values of Inflows/Present values of outflows = 1786.1/1400 = 1.28

(b).

MIRR = n root of (FV(Positive Cash flows, Cost of Capital)/PV(Initialoutlay, Financing Cost))-1

4 root of(1786.1/1400) -1 = 1.28^1/4 -1 = 1.063 -1= .063 or 6.3%

(c).

Since IRR of incremental cash flows of proct X over Y is 19.41%, Above 19.41% DF, Project Y shall be accepted and vice versa.

Cash flows Year( N) X DF @ 12% PV 0 -1400 1 -1400.0 1 350 0.893 312.5 2 750 0.797 597.9 3 650 0.712 462.7 4 650 0.636 413.1 NPV 386.1

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