Question

Please do in excel showing the work Wansley Lumber is considering the purchase of a paper company, which would require an initial investment of $300 million. Wansley estimates that the paper company would provide net cash flows of $40 million at the end of each of the next 20 years. The cost of capital for the paper company is 13%. a. Should Wansley purchase the paper company? b. Wansley realizes that the cash flows in Years 1 to 20 might be $30 million per year or $50 million per year, with a 50% probability of each outcome. Because of the nature of the purchase contract, Wansley can sell the company 2 years after purchase (at Year 2 in this case) for $280 million if it no longer wants to own it. Given this additional information, does decision-tree analysis indicate that it makes sense to purchase the paper company? Again, assume that all cash flows are discounted at 13%. c. Wansley can wait for 1 year and find out whether the cash flows will be $30 million per year or $50 million per year before deciding to purchase the company. Because of the nature of the purchase contract, if it waits to purchase, Wansley can no longer sell the company 2 years after purchase. Given this additional information, does decision-tree analysis indicate that it makes sense to purchase the paper company? If so, when? Again, assume that all cash flows are discounted at 13%.

Answer 1

Discounting factor:

where,

n= the respective year

Part a:

Cost of capital= 13%

Year	Cash flow (i)	Discount factor @13% (ii)	Net Present Value (i)x(ii)
0	-300000000	1	-300000000
1	40000000	0.884956	35398230.09
2	40000000	0.783147	31325867.33
3	40000000	0.69305	27722006.49
4	40000000	0.613319	24532749.11
5	40000000	0.54276	21710397.44
6	40000000	0.480319	19212741.1
7	40000000	0.425061	17002425.75
8	40000000	0.37616	15046394.47
9	40000000	0.332885	13315393.34
10	40000000	0.294588	11783533.93
11	40000000	0.260698	10427906.13
12	40000000	0.230706	9228235.512
13	40000000	0.204165	8166580.099
14	40000000	0.180677	7227062.034
15	40000000	0.159891	6395630.119
16	40000000	0.141496	5659849.663
17	40000000	0.125218	5008716.516
18	40000000	0.110812	4432492.492
19	40000000	0.098064	3922559.727
20	40000000	0.086782	3471291.794
		NPV	-19009936.9

Since the net present value of all estimated future cashflows is negative, it is not recommended to purchase the company.

Part b:

AS given in question, probability of cash flows in years 1 to 20 to be $30,000,000 and $50,000,000 is 50:50, the NPV would come to be the same as that derived in part a where the cash flow is $40,000,000 per year.

Alternatively, the working can be understood as follows:

• If the cash flows in Years 1 to 20 might be $30 million per year :

Year	Cash flow (i)	Discount factor @13% (ii)	Net Present Value (i)x(ii)
0	-300000000	1	-300000000
1	30000000	0.884955752	26548672.57
2	30000000	0.783146683	23494400.5
3	30000000	0.693050162	20791504.87
4	30000000	0.613318728	18399561.83
5	30000000	0.542759936	16282798.08
6	30000000	0.480318527	14409555.82
7	30000000	0.425060644	12751819.31
8	30000000	0.376159862	11284795.85
9	30000000	0.332884833	9986545.001
10	30000000	0.294588348	8837650.444
11	30000000	0.260697653	7820929.596
12	30000000	0.230705888	6921176.634
13	30000000	0.204164502	6124935.074
14	30000000	0.180676551	5420296.526
15	30000000	0.159890753	4796722.589
16	30000000	0.141496242	4244887.247
17	30000000	0.125217913	3756537.387
18	30000000	0.110812312	3324369.369
19	30000000	0.098063993	2941919.795
20	30000000	0.086782295	2603468.846
		NPV	-89257452.66

• If the cash flows in Years 1 to 20 might be $50 million per year :

Year	Cash flow (i)	Discount factor @13% (ii)	Net Present Value (i)x(ii)
0	-300000000	1	-300000000
1	50000000	0.884955752	44247787.61
2	50000000	0.783146683	39157334.17
3	50000000	0.693050162	34652508.11
4	50000000	0.613318728	30665936.38
5	50000000	0.542759936	27137996.8
6	50000000	0.480318527	24015926.37
7	50000000	0.425060644	21253032.19
8	50000000	0.376159862	18807993.09
9	50000000	0.332884833	16644241.67
10	50000000	0.294588348	14729417.41
11	50000000	0.260697653	13034882.66
12	50000000	0.230705888	11535294.39
13	50000000	0.204164502	10208225.12
14	50000000	0.180676551	9033827.543
15	50000000	0.159890753	7994537.649
16	50000000	0.141496242	7074812.079
17	50000000	0.125217913	6260895.645
18	50000000	0.110812312	5540615.615
19	50000000	0.098063993	4903199.659
20	50000000	0.086782295	4339114.743
		NPV	51237578.9

Probability of cash flows being $30,000,000 and $50,000,000 if 50% each, therefore NPV=

(89257452.66*.5)+(51237578.9 *.5)

= -19009936.88

Since the estimated NPV is still negative, it is still recommended to not invest in the paper company.

• If the paper company is purchased and is to be sold by the end of year 2, the NPV still remains to be negative. Please refer the below table for working:

Year	Cash flow (i)	Discount factor @13% (ii)	Net Present Value (i)x(ii)
0	-300000000	1	-300000000
1	40000000	0.884955752	35398230.09
2	40000000	0.783146683	31325867.33
2	280000000	0.783146683	219281071.3
		NPV	-13994831.23

Hence, the suggestion is still the same. It is recommended to purchase the paper company.

Part C:

As per the questions, because of the nature of the purchase contract, if it waits to purchase, he can no longer sell the company after 2 years if Wansley waits for 1 year before deciding to purchase the company.

Therefore, if Wansley can wait for 1 year before deciding to purchase the company, it is recommended that he purchase the company only if the cash flows are $50,000,000. Since in this case the Net present value of all cash flows is positive.