# Tv inflows 600110 3 600110 2 850110 1 245960 now mirr

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TV inflows = \$600(1.10)3+ \$600(1.10)2+ \$850(1.10)1= \$2,459.60.Now, MIRR is that discount rate which forces the TV of \$2,459.60 in 7 years to equal\$978.82:\$952.00 = \$2,547.60(1+MIRR)7.MIRRA= 14.07%.Similarly, MIRRB= 15.89%.At r = 17%,MIRRA= 17.57%.MIRRB= 19.91%.e.To find the crossover rate, construct a Project ∆ which is the difference in the twoprojects' cash flows:Project ∆ =YearCFA- CFB0\$1051(521)2(327)3(234)4466546667167(180)IRR= Crossover rate = 14.53%.Projects A and B are mutually exclusive, thus, only one of the projects can be chosen.As long as the cost of capital is greater than the crossover rate, both the NPV and IRRmethods will lead to the same project selection.However, if the cost of capital is lessthan the crossover rate the two methods lead to different project selections--a conflictexists.When a conflict exists the NPV method must be used.Because of the sign changes and the size of the cash flows, Project ∆ has multipleIRRs.Thus, a calculator's IRR function willnot work.One could use the trial anderror method of entering different discount rates until NPV = \$0.However, an HPcan be "tricked" into giving the roots.After you have keyed Project Delta's cashflows into the g register of an HP-10B, you will see an "Error-Soln" message.Nowenter 10 - STOIRR/YR and the 14.53% IRR is found. Then enter 100STOIRR/YR to obtain IRR = 456.22%. Similarly, Excel or Lotus 1-2-3 can also be used.Mini Case:10 - 13
10-9a.Incremental CashYearPlan BPlan AFlow (B - A)0(\$10,000,000)(\$10,000,000)\$011,750,00012,000,000(10,250,000)2-201,750,00001,750,000If the firm goes with Plan B, it will forgo \$10,250,000 in Year 1, but will receive\$1,750,000 per year in Years 2-20.b.If the firm could invest the incremental \$10,250,000 at a return of 16.07%, it wouldreceive cash flows of \$1,750,000.If we set up an amortization schedule, we wouldfind that payments of \$1,750,000 per year for 19 years would amortize a loan of\$10,250,000 at 16.0665%.Financial calculator solution:Inputs19-1025000017500000Output= 16.0665c.Yes, assuming (1) equal risk among projects, and (2) that the cost of capital is aconstant and does not vary with the amount of capital raised.d.See graph.If the cost of capital is less than 16.07%, then Plan B should be accepted;if r > 16.07%, then Plan A is preferred.Mini Case:10 - 14NIFVPMTPVN P V ( M i l l i o n s o f D o l l a r s )BC r o s s o v e r R a t e = 1 6 . 0 7 %I R RB= 1 6 . 7 %I R RA= 2 0 %AC o s t o fC a p i t a l ( % )52 51 02 01 51 52 01 02 55
10-10a.Financial calculator solution:Plan AInputs201080000000Output= -68,108,510NPVA= \$68,108,510 - \$50,000,000 = \$18,108,510.Plan BInputs201034000000Output= -28,946,117NPVB= \$28,946,117 - \$15,000,000 = \$13,946,117.Plan AInputs20-5000000080000000Output= 15.03IRRA= 15.03%.Plan BInputs20-1500000034000000Output= 22.26IRRB= 22.26%.Mini Case:10 - 15NIFVPMTPVNIFVPMTPVNIFVPMTPVNIFVPMTPV
b.If the company takes Plan A rather than B, its cash flows will be (in millions ofdollars):Cash FlowsCash FlowsProject ∆Yearfrom Afrom BCash Flows0(\$50)(\$15.0)(\$35.0)183.44.6283.44.6............2083.44.6So, Project ∆ has a "cost" of \$35,000,000 and "inflows" of \$4,600,000 per year for 20years.

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