Question

3. You are considering two mutually exclusive projects with the following cash flows. Which project(s) should you accept if the discount rate is 8.5 percent? What if the discount rate is 13 percent? Year Project A Project B -$80,000 -$80,000 31,000 31,000 0 31,000 110,000 A. accept project A as it always has the higher NPV B. accept project B as it always has the higher NPV C. accept A at 8.5 percent and B at 13 percent D. accept B at 8.5 percent and A at 13 percent E. accept B at 8.5 percent and neither at 13 percent

Answer 1

Project A Discount Discounted Discounted Cash Discount Factor Cash flows Factor @ Cash flows @ Year flows @ 8.5% @ 13% 8.5% 13% (80,000) (80,000.00) (80,000) 0 1 31,000 27,434 1 0.9217 28,571.43 0.8850 26,333.11 0.7831 2 31,000 0.8495 24,278 0.7829 24,270.15 3 31,000 0.6931 21,485 (6,804) (825.31) NPV Project B Discounted Discount Discounted Cash Discount Factor Cash flows @ Cash flows Factor @ Year flows @ 8.5% 13% 8.5% 13% (80,000) (80,000.00) (80,000) 0 1 1 0.8850 1 0.9217 0.8495 2 0.7831 110,000 86,119.89 76,236 3 0.7829 0.6931 (3,764) NPV 6,119.89

NPV is the difference between discounted cash inflows and discounted cash outflows.

From the above, we can see that only Project B at 8.5% gives postive NPV.

So Project B at 8.5% must be accepted and not at 13.5%

Answer: B: Accept project B as it has higher NPV

4.

Required Rate at 13% Discounted Discount Cash flows Cash flows @ Year Factor @ 13% 13% (42,000) (42,000.00) 0 1 1 15,300 0.8850 13,539.82 2 28,400 0.7831 22,241.37 7,500 0.6931 5,197.88 (1,020.93) Total 4

Discounted Discount Discount Discounted Cash flows Cash flows Cash flows Factor @ Factor @ Year 11% @ 11% 13% @ 13% 15,300 1 0.9009 13,783.78 0.8850 13,539.82 2 28,400 0.8116 23,050.08 0.7831 22,241.37 7,500 0.7312 5,483.94 0.6931 5,197.88 Total 42,317.80 40,979.07

We used trial and error method to calculate IRR, we take one rate (13%) which discounts to less than actual cash outflow and other rate (11%) which discounts to greater than actual cash flow. You can chose any other rates but the closer these rates to the IRR the more accurate the result will be.

$IRR = 11 + \frac{42317.80-42000}{42317.80-40979.07}*(13-11)$

$= 11 + \frac{317.80}{1338.73}*2$

Therefore, IRR = 11.47%

Which is lesser than required rate of return by 1.53% .........(13%-11.47%)

So answer is: B: No; The IRR is less than the required return by about 1.53 percent.

Other formulas used in calculations:

$Discount~factor = \frac{1}{(1+i)^n}$

Where ,

i = rate of return

n = number of periods