Question

Problem 4-12 Present Value and Multiple Cash Flows Investment X offers to pay you $4,900 per year for nine years, whereas Investment Y offers to pay you $7,600 per year for five years. Calculate the present value for Investments X and Y if the discount rate is 4 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present value Investment X $ Investment Y $ Calculate the present value for Investments X and Y if the discount rate is 14 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present value Investment X $ Investment Y $

Answer 1

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Computation of present value with 4% discount rate
i	ii	iii	iv		v=ii*iv	vi=iii*iv
Year	Cash flow X	Cash flow Y	PVIF @ 4%		Present value X	Present value Y
1	$   4,900.00	$       7,600.00	0.961538		$        4,711.54	$        7,307.69
2	$   4,900.00	$       7,600.00	0.924556		$        4,530.33	$        7,026.63
3	$   4,900.00	$       7,600.00	0.888996		$        4,356.08	$        6,756.37
4	$   4,900.00	$       7,600.00	0.854804		$        4,188.54	$        6,496.51
5	$   4,900.00	$       7,600.00	0.821927		$        4,027.44	$        6,246.65
6	$   4,900.00		0.790315		$        3,872.54	$                    -
7	$   4,900.00		0.759918		$        3,723.60	$                    -
8	$   4,900.00		0.73069		$        3,580.38	$                    -
9	$   4,900.00		0.702587		$        3,442.68	$                    -
					$      36,433.12	$      33,833.85
therefore
PV X =	$ 36,433.12
PV Y =	$ 33,833.85
Computation of present value with 14% discount rate
i	ii	iii	iv		v=ii*iv	vi=iii*iv
Year	Cash flow X	Cash flow Y	PVIF @ 14%		Present value X	Present value Y
1	$   4,900.00	$       7,600.00	0.877193		$        4,298.25	$        6,666.67
2	$   4,900.00	$       7,600.00	0.769468		$        3,770.39	$        5,847.95
3	$   4,900.00	$       7,600.00	0.674972		$        3,307.36	$        5,129.78
4	$   4,900.00	$       7,600.00	0.59208		$        2,901.19	$        4,499.81
5	$   4,900.00	$       7,600.00	0.519369		$        2,544.91	$        3,947.20
6	$   4,900.00		0.455587		$        2,232.37	$                    -
7	$   4,900.00		0.399637		$        1,958.22	$                    -
8	$   4,900.00		0.350559		$        1,717.74	$                    -
9	$   4,900.00		0.307508		$        1,506.79	$                    -
					$      24,237.22	$      26,091.42
therefore
PV X =	$ 24,237.22
PV Y =	$ 26,091.42