Question

Dark Skies Observatory is considering several options to purchase a new deep-space telescope. Revenue would be generated from the telescope by selling "time and use" slots to various researchers around the world. Four possible telescopes have been identified in addition to the possibility of not buying a telescope if none are financially attractive. The table below details the characteristics of each telescope. An external rate of return analysis is to be performed using a MARR of 25%. T1 T2 T3 T4 Useful Life 10 years 10 years 10 years 10 years First Cost $600,000 $800,000 $470,000 $540,000 Salvage Value $70,000 $130,000 $65,000 $200,000 Annual Revenue $400,000 $600,000 $260,000 $320,000 Annual Expenses $130,000 $270,000 $70,000 $120,000 Which telescope (if any) is most financially attractive? Show the comparisons and external rates of return used to reach this decision: Comparison 1: Comparison 2: ERR 1: ERR 2: ERR 3: ERR 4: Comparison 3: Comparison 4:

Answer 1

		MARR=25%
			T1	T2	T3	T4
		Useful Life	10	10	10	10
	A	First Cost	$600,000	$800,000	$470,000	$540,000
	B	Salvage Value	$70,000	$130,000	$65,000	$200,000
	C	Annual Revenue	$400,000	$600,000	$260,000	$320,000
	D	AnnualExpenses	$130,000	$270,000	$70,000	$120,000
	E=C-D	Annual Cash inFlow Year1-9	$270,000	$330,000	$190,000	$200,000
	F=C-D+B	Cash Inflow in Year 10	$340,000	$460,000	$255,000	$400,000
		EXTERNAL RATE OF RETURN=R
		First Cost*(1+R)^10= Future Value of Annual Cash Inflows at end of 10 years
		Future Value(FV) of Cash Flow at end of 10 years=(Cash Flow)*((1+i)^(10-N))
		i=MARR=25%=0.25
		EXTERNAL RATE OF RETURN OF T1
	N	Year	1	2	3	4	5	6	7	8	9	10
	CF	Cash Flow	$270,000	$270,000	$270,000	$270,000	$270,000	$270,000	$270,000	$270,000	$270,000	$340,000	SUM
	FV=CF*(1.25^(10-N))	Future Value of Cash Flow at year10	$2,011,657	$1,609,325	$1,287,460	$1,029,968	$823,975	$659,180	$527,344	$421,875	$337,500	$340,000	$9,048,284
	G	Future Value of all Cash In Flows	$9,048,284
	H	First Cost	$600,000
		(1+R)^10=G/H	15.08047301
		1+R=	1.311721075
		EXTERNAL RATE OF RETURN OF T1	0.311721075
		EXTERNAL RATE OF RETURN OF T1	31.17%
		EXTERNAL RATE OF RETURN OF T2
	N	Year	1	2	3	4	5	6	7	8	9	10
	CF	Cash Flow	$330,000	$330,000	$330,000	$330,000	$330,000	$330,000	$330,000	$330,000	$330,000	$460,000	SUM
	FV=CF*(1.25^(10-N))	Future Value of Cash Flow at year10	$2,458,692	$1,966,953	$1,573,563	$1,258,850	$1,007,080	$805,664	$644,531	$515,625	$412,500	$460,000	$11,103,458
	G	Future Value of all Cash In Flows	$11,103,458
	H	First Cost	$800,000
		(1+R)^10=G/H	13.87932248
		1+R=	1.300878771
		EXTERNAL RATE OF RETURN OF T2	0.300878771
		EXTERNAL RATE OF RETURN OF T2	30.09%
		EXTERNAL RATE OF RETURN OF T3
	N	Year	1	2	3	4	5	6	7	8	9	10
	CF	Cash Flow	$190,000	$190,000	$190,000	$190,000	$190,000	$190,000	$190,000	$190,000	$190,000	$255,000	SUM
	FV=CF*(1.25^(10-N))	Future Value of Cash Flow at year10	$1,415,610	$1,132,488	$905,991	$724,792	$579,834	$463,867	$371,094	$296,875	$237,500	$255,000	$6,383,052
	G	Future Value of all Cash In Flows	$6,383,052
	H	First Cost	$470,000
		(1+R)^10=G/H	13.58096078
		1+R=	1.298054866
		EXTERNAL RATE OF RETURN OF T3	0.298054866
		EXTERNAL RATE OF RETURN OF T3	29.81%
		EXTERNAL RATE OF RETURN OF T4
	N	Year	1	2	3	4	5	6	7	8	9	10
	CF	Cash Flow	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$400,000	SUM
	FV=CF*(1.25^(10-N))	Future Value of Cash Flow at year10	$1,490,116	$1,192,093	$953,674	$762,939	$610,352	$488,281	$390,625	$312,500	$250,000	$400,000	$6,850,581
	G	Future Value of all Cash In Flows	$6,850,581
	H	First Cost	$540,000
		(1+R)^10=G/H	12.68626036
		1+R=	1.289238785
		EXTERNAL RATE OF RETURN OF T4	0.289238785
		EXTERNAL RATE OF RETURN OF T4	28.92%