Question

Considering discount rate of 14%, calculate NPV, Benefit Cost Ratio, and Present Value Ratio for the following investment and explain if it is a good investment.

C=10,000	C=8,000	C=6,000	I=7,500	I=7,500	...	I=7,500	L=10,000
0	1	2	3	4	...	10

C: Cost, I:Income, L: Salvage value

Answer 1

Let us look at the table below:

Year	CF	Discount Factor		Discounted CF
0	-10000	1/1.14^0=	1	-10000*1=	-10000
1	-8000	1/1.14^1=	0.877193	-8000*0.87719298245614=	-7017.54
2	-6000	1/1.14^2=	0.769468	-6000*0.769467528470299=	-4616.81
3	7500	1/1.14^3=	0.674972	7500*0.674971516202016=	5062.286
4	7500	1/1.14^4=	0.59208	7500*0.59208027737019=	4440.602
5	7500	1/1.14^5=	0.519369	7500*0.519368664359816=	3895.265
6	7500	1/1.14^6=	0.455587	7500*0.455586547684049=	3416.899
7	7500	1/1.14^7=	0.399637	7500*0.399637322529867=	2997.280
8	7500	1/1.14^8=	0.350559	7500*0.350559054850761=	2629.193
9	7500	1/1.14^9=	0.307508	7500*0.307507942851545=	2306.310
10	7500	1/1.14^10=	0.269744	7500*0.269743809518899=	2023.079
10	10000	1/1.14^10=	0.269744	10000*0.269743809518899=	2697.438
NPV = Sum of all PV					7834.003
Benefits Cost Ratio					1.362109
Present Value Ratio					0.362109

• As the CF for years 1-3 are costs, they are outflows and therefore negative
• As the CF for years 4-10 are incomes, they are inflows and therefore positive
• As the salvage value is an inflow therefore it is positive
• NPV = Sum of all discounted CF
• Benefits cost ratio = Sum of Positive discounted CF/Sum of Negative discounted CF
• Present Value ratio = NPV/Sum of Negative discounted CF