Question

In: Accounting

Consider the following investment offers regarding a product you have recently developed. A 10% interest rate...

Consider the following investment offers regarding a product you have recently developed. A 10% interest rate should be used throughout this analysis unless otherwise specified:

Offer (I) – Receive $0.57m now and $197k from year 6 through 15. Also, if your product achieved over $100 million in cumulative sales by the end of year 15, you would receive an additional $3m. Assume that there is a 70% probability this would happen.

Offer (II) – Receive 30% of the buyer’s gross profit on the product for the next 4 years. Assume that the buyer’s gross profit margin is 60%. Sales in year 1 are projected to be $1.9m and then expected to grow by 40% per year.

Offer (III) – A trust fund would be set up, calling for semiannual payments of $206k for 8 years. On the 17th period, you would receive the compounded proceeds, which would then be discounted over the 8-year period back to the present at the specified annual rate.

Note: The term “k” is used to represent thousands (× $1,000).

Required: Determine the percentage difference between your most and least profitable alternatives, with the least profitable option as the basis for your calculation.

Solutions

Expert Solution

Offer 1
Year Amount PVF @ 10 % Present Value
0 570000 1 570000
1 0.9091 0
2 0.8264 0
3 0.7513 0
4 0.683 0
5 0.6209 0
6 197000 0.5645 111206.5
7 197000 0.5132 101100.4
8 197000 0.4655 91703.5
9 197000 0.4241 83547.7
10 197000 0.3855 75943.5
11 197000 0.3505 69048.5
12 197000 0.3186 62764.2
13 197000 0.2897 57070.9
14 197000 0.2633 51870.1
15 2297000 0.2394 549901.8
Total Present Value 1824157.1
Offer 2
Year Sales Gross Profit Amount Received PVF @10 % Present Value
(40% increase
from last year)
Sales * 40% Gross Profit * 30%
0
1 1900000 1140000 342000 0.9091 310912.2
2 2660000 1596000 478800 0.8264 395680.32
3 3724000 2234400 670320 0.7513 503611.416
4 5213600 3128160 938448 0.683 640959.984
Total present Value 1851163.92
Offer 3
Interest Rate 0.1
Year Amount Future Value Present Value
0
1 206000 449672.1652 2276079.322
2 206000 428259.205
3 206000 407865.9095
4 206000 388443.7233
5 206000 369946.4032
6 206000 352329.9078
7 206000 335552.2931
8 206000 319573.6125
9 206000 304355.8214
10 206000 289862.6871
11 206000 276059.702
12 206000 262914.0019
13 206000 250394.2875
14 206000 238470.75
15 206000 227115
16 206000 216300
17 206000 5117115.469

Percentage Difference between most and least proftable alternatives

2276079 - 1824157 / 1824157 = 24.774 %

Note

Offer 3 - Formula used in excel to calculate Future value and Present value is shown in the image attached below

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