Question

q.1

Discounted payback

period.

​Becker, Inc. uses the discounted payback period for projects costing less than​ $25,000 and has a cutoff period of four years for these​ small-value projects. Two​ projects, R and​ S, are under consideration. Their anticipated cash flows are listed in the following table. If Becker uses a discount rate of

4 %4%

on these​ projects, are they accepted or​ rejected? If it uses a discount rate of

12 %12%​?

A discount rate of

18 %18%​?

Why is it necessary to look at only the first four years of the​ projects' cash​ flows?

Cash Flow	Project R		Project S
Initial Cost	​ $20 comma 00020,000		​$17 comma 00017,000
Cash flow year 1	​$4 comma 0004,000		​$8 comma 5008,500
Cash flow year 2	​$6 comma 0006,000		​$6 comma 8006,800
Cash flow year 3	​$8 comma 0008,000		​$5 comma 1005,100
Cash flow year 4	​$10 comma 00010,000		​$3 comma 4003,400

With a discount rate of

44​%,

the cash outflow for project R​ is: ​ (Select the best​ response.)

A.

fully recovered in 3 years comma so reject.fully recovered in 3 years, so reject.

B.

fully recovered in 5​ years, so accept.

C.

fully recovered in 4 years comma so accept.fully recovered in 4 years, so accept.

D.

not fully recovered in four​ years, so reject.

q.2

Net present

value.

Quark Industries has three potential​ projects, all with an initial cost of

​$1 comma 900 comma 0001,900,000.

The capital budget for the year will allow Quark to accept only one of the three projects. Given the discount rate and the future cash flow of each​ project, determine which project Quark should accept.

Cash Flow	Project M		Project N		Project O
Year 1	​ $500 comma 000500,000		​$600 comma 000600,000		​$1 comma 000 comma 0001,000,000
Year 2	​$500 comma 000500,000		​$600 comma 000600,000		​$800 comma 000800,000
Year 3	​$500 comma 000500,000		​$600 comma 000600,000		​$600 comma 000600,000
Year 4	​$500 comma 000500,000		​$600 comma 000600,000		​$400 comma 000400,000
Year 5	​$500 comma 000500,000		​$600 comma 000600,000		​$200 comma 000200,000
Discount rate	88​%		1111​%		1616​%

Which project should Quark​ accept?  ​(Select the best​ response.)

A.

Project Upper NProject N

B.

Project Upper OProject O

C.

Project Upper MProject M

D.

None of the projects

q.3

Profitability

index.

Given the discount rate and the future cash flow of each project listed in the following​ table, use the PI to determine which projects the company should accept.

Cash Flow	Project U		Project V
Year 0	minus−​$1 comma 900 comma 0001,900,000		minus−​$2 comma 500 comma 0002,500,000
Year 1	​$475 comma 000475,000		​$1 comma 250 comma 0001,250,000
Year 2	​$475 comma 000475,000		​$1 comma 000 comma 0001,000,000
Year 3	​$475 comma 000475,000		​$750 comma 000750,000
Year 4	​$475 comma 000475,000		​$500 comma 000500,000
Year 5	​$475 comma 000475,000		​$250 comma 000250,000
Discount rate	77​%		1414​%

What is the PI of project​ U?

nothing  

​(Round to two decimal​ places.)

4.

MIRR unequal

lives.

Grady Enterprises is looking at two project opportunities for a parcel of land the company currently owns. The first project is a​ restaurant, and the second project is a sports facility. The projected cash flow of the restaurant is an initial cost of

​$1 comma 570 comma 0001,570,000

with cash flows over the next six years of

​$180 comma 000180,000

​(year one),

​$280 comma 000280,000

​(year two),

$ 260 comma 000$260,000

​(years three through​ five), and

​$1 comma 740 comma 0001,740,000

​(year six), at which point Grady plans to sell the restaurant. The sports facility has the following cash​ flows: an initial cost of

​$2 comma 440 comma 0002,440,000

with cash flows over the next four years of

​$370 comma 000370,000

​(years one through​ three) and

​$2 comma 560 comma 0002,560,000

​(year four), at which point Grady plans to sell the facility. The appropriate discount rate for the restaurant is

10.510.5​%

and the appropriate discount rate for the sports facility is

11.511.5​%.

What are the MIRRs for the Grady Enterprises​ projects? What are the MIRRs when you adjust for the unequal​ lives? Do the MIRR adjusted for unequal lives change the decision based on the​ MIRRs? ​Hint: Take all cash flows to the same ending period as the longest project.

If the appropriate reinvestment rate for the restaurant is

10.510.5​%,

what is the MIRR of the restaurant​ project?

nothing​%

​(Round to two decimal​ places.)

Answer 1

		Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=discount rate
		N=Year   of Cash Flow
		CASH FLOW ANALYSIS OF PROJECT R
	N	Year	0	1	2	3	4
	a	Cash Flow	-$20,000	$                4,000	$                6,000	$                8,000	$      10,000
	PV4=a/(1.04^N)	Present Value at discount rate 4%(0.04)	-$20,000	$3,846	$5,547	$7,112	$8,548
	CPV4	Cumulative Present Value at discount rate4%	-$20,000	-$16,154	-$10,607	-$3,495	$5,054
	PV12=a/(1.12^N)	Present Value at discount rate 12%(0.12)	-$20,000	$3,571	$4,783	$5,694	$6,355
	CPV12	Cumulative Present Value at discount rate12%	-$20,000	-$16,429	-$11,645	-$5,951	$404
	PV18=a/(1.18^N)	Present Value at discount rate 18%(0.18)	-$20,000	$3,390	$4,309	$4,869	$5,158
	CPV18	Cumulative Present Value at discount rate4%	-$20,000	-$16,610	-$12,301	-$7,432	-$2,274
	PV44=a/(1.44^N)	Present Value at discount rate 44%(0.44)	-$20,000	$2,778	$2,894	$2,679	$2,326
	CPV44	Cumulative Present Value at discount rate44%	-$20,000	-$17,222	-$14,329	-$11,650	-$9,324
		At Discount Rate of 4% Project R is accepted	Cumulative Present Value is POSITIVE
		At Discount Rate of 12% Project R is accepted	Cumulative Present Value is POSITIVE
		At Discount Rate of 18% Project R is Rejected	Cumulative Present Value is NEGATIVE
		At discount rate 44%, Cash flow is not fully recovered in 4 years, so reject
		CASH FLOW ANALYSIS OF PROJECT S
	N	Year	0	1	2	3	4
	a	Cash Flow	-$17,000	$                8,500	$                6,800	$                5,100	$        3,400
	PV4=a/(1.04^N)	Present Value at discount rate 4%(0.04)	-$17,000	$8,173	$6,287	$4,534	$2,906
	CPV4	Cumulative Present Value at discount rate4%	-$17,000	-$8,827	-$2,540	$1,994	$4,900
	PV12=a/(1.12^N)	Present Value at discount rate 12%(0.12)	-$17,000	$7,589	$5,421	$3,630	$2,161
	CPV12	Cumulative Present Value at discount rate12%	-$17,000	-$9,411	-$3,990	-$360	$1,801
	PV18=a/(1.18^N)	Present Value at discount rate 18%(0.18)	-$17,000	$7,203	$4,884	$3,104	$1,754
	CPV18	Cumulative Present Value at discount rate4%	-$17,000	-$9,797	-$4,913	-$1,809	-$55
	PV44=a/(1.44^N)	Present Value at discount rate 44%(0.44)	-$17,000	$5,903	$3,279	$1,708	$791
	CPV44	Cumulative Present Value at discount rate44%	-$17,000	-$11,097	-$7,818	-$6,110	-$5,319
		At Discount Rate of 4% Project R is accepted	Cumulative Present Value is POSITIVE
		At Discount Rate of 12% Project R is accepted	Cumulative Present Value is POSITIVE
		At Discount Rate of 18% Project R is Rejected	Cumulative Present Value is NEGATIVE
		At discount rate 44%, Cash flow is not fully recovered in 4 years, so reject