Question

J & J Enterprises is considering a cash acquisition of Patterson Steel Company for $6,200,000. Patterson will provide the following pattern of cash inflows and synergistic benefits for the next 20 years. There is no tax loss carryforward. Use Appendix D as an approximate answer, but calculate your final answer using the formula and financial calculator methods. Years 1–5 6–15 16–20 Cash inflow (aftertax) $660,000 $820,000 $935,000 Synergistic benefits (aftertax) 62,000 82,000 92,000 The cost of capital for the acquiring firm is 13 percent. a. Compute the net present value. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) b. Should the merger be undertaken? No Yes

Answer 1

a) Net present value (NPV) = Present value (P. V) of cash inflows - P. V. Of cash outflows

P. V. Of cash outflow (Acquisition cost) = $62,00,000

P. V. Of cash inflows = Annual cash flows for 1st 5 years * Annual P. V factor for 1st factor + (Annual cash flows for next 10 years * (Annual P. V. Factor upto 15 years - Annual P. V factor for 1st 5 years)) +( Annual cash flows for next 5 years * (Annual P. V factor upto 20 years - Annual P. V factor upto 15 years))

Here,

Annual P. V factor = (1 - (1/(1+i)^n)) / i)

i (Cost of capital) = 13% or 0.13

n = No. Of years

Now,

i) P. V of cash inflows for 1st 5 years = ($6,60,000 + $62,000) * ((1 - (1/(1+0.13)^5)) / 0.13)

P. V. Of cash inflows for 1st 5 years = $7,22,000 * ((1 - 0.5428) / 0.13)

P. V. of cash inflows for 1st 5 years = $7,22,000 * 3.52

P. V. of cash inflows for 1st 5 years = $25,41,440

ii) P. V of cash inflows for next 10 years = ($8,20,000 + $82,000) * (((1 - (1/(1+0.13)^15))/0.13) - ((1 - (1/(1+0.13)^5))/0.13))

P. V. Of cash inflows for next 10 years = $9,02,000 * (((1 - 0.1599)/0.13) - ((1 - 0.5428)/0.13))

P. V. Of cash inflows for next 10 years = $9,02,000 * (6.4623 - 3.5169)

P. V. Of cash inflows for next 10 years = $9,02,000 * 2.9454

P. V of cash inflows for next 10 years = $26,56,750.80

iii) P. V. Of cash inflows for last 5 years = ($9,35,000 + $92,000) * (((1 - (1/(1+0.13)^20))/0.13) - ((1 - (1/(1+0.13)^15))/0.13))

P. V. Of cash inflows for last 5 years = $10,27,000 * (((1 - (1/(1+0.13)^20))/0.13) - ((1 - (1/(1+0.13)^15))/0.13))

P. V. Of cash inflows for last 5 years = $10,27,000 * (((1 - 0.0868)/0.13) - ((1 - 0.1599)/0.13))

P. V of cash inflows for last 5 years = $10,27,000 * (7.0246 - 6.4623)

P. V. Of cash inflows for last 5 years = $10,27,000 * 0.5623

P. V. Of cash inflows for last 5 years = $5,77,482.10

Now,

Total P. V. Of caah inflows = $25,41,440 + $26,56,750.80 + $5,77,485.10

Total P. V. Of cash inflows = $57,75,675.90

Using the NPV formula,

NPV (Net present value) = $57,75,675.90 - $62,00,000

NPV = - $4,24,324.10

b) No, merger should not be undertaken.

Reason : As it's NPV is negative ie. loss on acquisition & hence merger should not be undertaken.