Question

An investor invests $11000. The investment pays $4000 at the end of year 1, $5000 at the end of year 2 and $4500 at the end of year 3. (a) Calculate the internal rate of return (IRR) of the investment. (b) Calculate the net present value (NPV) of the investment using interest preference rate of 8.5%.

Show all works, and please calculate it with math formula instead of financial calculator!! Thank you!

Answer 1

Calculation of NPV		8.50%
Year	Cash flow		PV factor, 1/(1+r)^t	PV-Board game
0	$         (11,000)		1.0000	$    (11,000.00)
1	$            4,000		0.9217	$       3,686.64
2	$            5,000		0.8495	$       4,247.28
3	$            4,500		0.7829	$       3,523.09
			NPV	$          457.00
Calculation of IRR	10%	11%
Year	Cash flow	PV factor, 1/(1+r)^t	PV factor, 1/(1+r)^t	PV@10%	PV@11%
0	$         (11,000)	1.0000	1.0000	$    (11,000.00)	$(11,000.00)
1	$            4,000	0.9091	0.9009	$       3,636.36	$    3,603.60
2	$            5,000	0.8264	0.8116	$       4,132.23	$    4,058.11
3	$            4,500	0.7513	0.7312	$       3,380.92	$    3,290.36
			NPV	$          149.51	$       (47.92)
		IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
		IRR	'=10%+ (11%-10%)*(149.51/(149.51+47.92)
		IRR	10.76%