Question

Carter Company owns a plot of land on which buried toxic wastes have been discovered. Since it will require several years and a considerable sum of money before the property is fully detoxified and capable of generating revenues, Carter wishes to sell the land now. It has located four potential buyers: Buyer A, who is willing to pay $255,000 for the land now; Buyer B, who is willing to make 20 annual payments of $40,000 each, with the first payment to be made 5 years from today; Buyer C, who is willing to make 10 semi-annual payments of $32,000, with the first payment to be made today; and Buyer D, who is willing to make two payments of $150,000, the first to be made today and the second to be paid three years from today. INSTRUCTIONS Calculate the present value of each of the options, assuming that the appropriate rate of interest is 8%. Show all calculations. To whom should Carter sell the land? A:________________ B:________________ C:________________ D:________________

Answer 1

Answer)

Present Value of Payments of different Buyers

(Amount in $)

Particulars	Buyer A	Buyer B	Buyer C	Buyer D
Present Value of Payment	2,55,000.00	2,88,665.26	2,69,930.61	2,69,074.84

Conclusion: Since present value of amount offered by Buyer B is highest, Carter should sell the land to Buyer B

Workings:

Buyer A: Since buyer A is making the entire payment of $ 255,000, the present value factor for today will be ‘1’.

Present Value= Amount received x PVF (0 year, 8% p.a.)

                          = $ 255,000 x 1

                          = $ 255,000.

Therefore, present value of cash flow from Buyer A will be $ 255,000.

Buyer B: Since buyer B is going to make 20 annual payments of $ 40,000 each, Present value will be calculated by Deducting Present Value Annuity Factor (PVAF) for 4 years at 8% from Present Value Annuity Factor (PVAF) for 24 years at 8% and multiplying the resultant figure by annual cash flow.

Note: Present Value Annuity Factor is the aggregate of Present value factors for given number of years at given rate of interest.

Present Value = [PVAF (24 years, 8% p. a.) – PVAF (first 4 years, 8% p.a.)] x $ 40,000

                       = [10.5288 – 3.3121] x $ 40,000

                      = 7.2166 x $ 40,000

                      = $ 288,665.26

Alternatively, it can be calculated as follows:

End of Year	Annual Cash Flow	PVF at 8%	Present Value
1	-	0.9259	-
2	-	0.8573	-
3	-	0.7938	-
4	-	0.7350	-
5	40,000	0.6806	27,223.33
6	40,000	0.6302	25,206.79
7	40,000	0.5835	23,339.62
8	40,000	0.5403	21,610.76
9	40,000	0.5002	20,009.96
10	40,000	0.4632	18,527.74
11	40,000	0.4289	17,155.31
12	40,000	0.3971	15,884.55
13	40,000	0.3677	14,707.92
14	40,000	0.3405	13,618.44
15	40,000	0.3152	12,609.67
16	40,000	0.2919	11,675.62
17	40,000	0.2703	10,810.76
18	40,000	0.2502	10,009.96
19	40,000	0.2317	9,268.48
20	40,000	0.2145	8,581.93
21	40,000	0.1987	7,946.23
22	40,000	0.1839	7,357.62
23	40,000	0.1703	6,812.61
24	40,000	0.1577	6,307.97
Total			288,665.26

  

Therefore, present value of cash flow from Buyer B will be $ 288,665.26

Buyer C: Since Buyer C is making Semi annual payments, the semi-annual rate of interest will be 4% (i.e. 8%/2).Thus Present value of cash flows will be calculated as follows:

Present Value = [PVF (0^th period, 4%) x $ 32,000] +[ PVAF (9 periods, 4%) x $ 32,000]

                           = [1 x $ 32,000] + [7.4353 x $ 32,000]

                           = $ 32,000 + $ 237,930.61

                        = $ 269,930.61

Alternatively, it can be calculated as follows:

End of Period	Annual Cash Flow	PVF at 4%	Present Value
0	32000	1.0000	32,000.00
1	32000	0.9615	30,769.23
2	32000	0.9246	29,585.80
3	32000	0.8890	28,447.88
4	32000	0.8548	27,353.73
5	32000	0.8219	26,301.67
6	32000	0.7903	25,290.06
7	32000	0.7599	24,317.37
8	32000	0.7307	23,382.09
9	32000	0.7026	22,482.78
Total			2,69,930.61

Therefore, present value of cash flow from Buyer C will be $ 269,930.61.

Buyer D: Buyer D will make two equal payments of $ 150,000. One payment today and the other at the end of year 3.

Present value = [PVF (year 0, 8% p.a.) + PVF (year 3, 8% p.a.)] x $ 150,000

                       = [1.00 + 0.7938] x $ 150,000

                       = $ 269,074.84 Approx.

Alternatively, it can be calculated as follows:

End of Year	Annual Cash Flow	PVF at 8%	Present Value
0	1,50,000.0	1.0000	1,50,000.00
1	-	0.9259	-
2	-	0.8573	-
3	1,50,000.0	0.7938	1,19,074.84
Total			2,69,074.84

Therefore, present value of cash flow from Buyer D will be $ 269,074.84.