Question

3. You are considering the following two mutually exclusive projects. The crossover point (the discount rate at which the two projects have the same NPV) is_ percent. (Note: Trial and error may be the fastest and easiest way to find the correct answer) Year Project A Project B O -$32,000 -$32,000 18,000 12,000 13,000 13,000 9,000 16,000 7.7.86% b.7.92% c. 8.01% d. 8.12% e. 8.35%

Answer 1

If rate is 7.86%
Year	Project A Cash flow	Present value formula	Present value		Year	Project B Cash flow	Present value formula	Present value
0	-32,000	-32,000	-32,000		0	-32,000	-32,000	-32,000
1	18,000	=18000/(1+7.86%)^1	16,688		1	12,000	=12000/(1+7.86%)^1	11,126
2	13,000	=13000/(1+7.86%)^2	11,174		2	13,000	=13000/(1+7.86%)^2	11,174
3	9,000	=9000/(1+7.86%)^3	7,172		3	16,000	=16000/(1+7.86%)^3	12,751
		NPV	3,035				NPV	3,051
If rate is 7.92%
Year	Project A Cash flow	Present value formula	Present value		Year	Project B Cash flow	Present value formula	Present value
0	-32,000	-32,000	-32,000		0	-32,000	-32,000	-32,000
1	18,000	=18000/(1+7.92%)^1	16,679		1	12,000	=12000/(1+7.92%)^1	11,119
2	13,000	=13000/(1+7.92%)^2	11,162		2	13,000	=13000/(1+7.92%)^2	11,162
3	9,000	=9000/(1+7.92%)^3	7,160		3	16,000	=16000/(1+7.92%)^3	12,730
		NPV	3,001				NPV	3,011
If rate is 8.01%
Year	Project A Cash flow	Present value formula	Present value		Year	Project B Cash flow	Present value formula	Present value
0	-32,000	-32,000	-32,000		0	-32,000	-32,000	-32,000
1	18,000	=18000/(1+8.01%)^1	16,665		1	12,000	=12000/(1+8.01%)^1	11,110
2	13,000	=13000/(1+8.01%)^2	11,143		2	13,000	=13000/(1+8.01%)^2	11,143
3	9,000	=9000/(1+8.01%)^3	7,143		3	16,000	=16000/(1+8.01%)^3	12,698
		NPV	2,951				NPV	2,951
Answer :
The crossover point is 8.01%