Question

Springfield Manufacturing Co. is considering the investment of $60,000 in a new machine. The machine will generate cash flow of $7,500 per year for each year of its 15 year life and will have a salvage value of $4,000 at the end of its life. Springfield's cost of capital is 10%.

(a.) Calculate the net present value of the proposed investment. Ignore income taxes, and round all answers to the nearest $1.
(b.) Calculate the present value ratio of the investment.
(c.) What will the internal rate of return on this investment be relative to the cost of capital? Explain your answer.
(d.) Calculate the payback period of the investment.

Answer 1

(a)
	Net Present Value		$ -1,997
	Working:
	a.	Present value of annuity of 1			=	(1-(1+i)^-n)/i		Where,
					=	(1-(1+0.10)^-15)/0.10		i	10%
					=	7.6061		n	15
	b.	Present value of 1			=	(1+i)^-n		Where,
					=	(1+0.10)^-15		i	10%
					=	0.2394		n	15
	c.	Present Value of annual cash flows			=	Annual Cash flows x Present Value of annuity of 1
					=	$               7,500	x	7.6061
					=	$            57,046
	d.	Present Value of salvage value			=	Salvage Value x Present value of 1
					=	$               4,000	x	0.2394
					=	$                  958
	e.	Present Value of annual cash flows				$            57,046
		Present Value of salvage value				$                  958
		Present value of cash inflows				$            58,003
		Less:Cost of Investment				$            60,000
		Net Present Value				$             -1,997
(b)
	Present Value Ratio		0.97
	Working:
	Present Value Ratio		=	Present Value of cash inflows/Present Value of Cash outflows
			=	$ 58,003	/	$            60,000
			=	0.97
(c)
	Internal rate of Return		9.43%
	Working;
	Internal Rate of Return (IRR) is the rate at which Net Present Value is zero.
	Year	Cash flows
	0	-60,000
	1	7,500
	2	7,500
	3	7,500
	4	7,500
	5	7,500
	6	7,500
	7	7,500
	8	7,500
	9	7,500
	10	7,500
	11	7,500
	12	7,500
	13	7,500
	14	7,500
	15	11,500
	IRR	=IRR(C48:C63)
		9.43%
	Internal rate of return is lower than cost of capital of Sprinfield.On the basis of IRR, project should be profiable.
	The Objective of Investment is to maximisation of wealth. In the current case Net Present value, Present Value Ratio and Internal rate of return
	is showing that project is not better to invest as Wealth will be reduced by going through this investment.
	So, Investor should not invest is this project.
(d)
	Payback Period		8 Years
	Working;
	Payback Period is the time upto which Initial cash investment is recovered back.
	Year	Cash flows	Cumulative Cash flows
	0	-60,000	-60,000
	1	7,500	-52,500
	2	7,500	-45,000
	3	7,500	-37,500
	4	7,500	-30,000
	5	7,500	-22,500
	6	7,500	-15,000
	7	7,500	-7,500
	8	7,500	0
	9	7,500	7,500
	10	7,500	15,000
	11	7,500	22,500
	12	7,500	30,000
	13	7,500	37,500
	14	7,500	45,000
	15	11,500	56,500
	In 8th Year, all of investment is recovered back. So, Payback period of the project is 8 Years.