#4: FAMILY BUSINESS EXAMPLE You own a family business with net worth of $250,000
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Question
#4: FAMILY BUSINESS EXAMPLE You own a family business with net worth of $250,000. You can purchase a machine costing $200,000 today (11/8/14) . If the market for the output remains strong, you will receive the following revenue stream (assume no additional costs): Revenue $80,000 $80,000 $80,000 $80,000 $80,000 Date 11/10/15 11/10/16 11/10/18 11/10/19 At the end of the period, the machine will have re-sale value of $1,000 (scrap metal). If the market is weak, you will receive the following revenue stream (assume no additional costs):Explanation / Answer
This case will have to be looked from the point of view of concepts of present value of money and also the probability of each economic scenario occurring (i.e. probability of a strong market or a weak market) will have to be considered.
We know that present value of a future cash flow = the amount of cash flow to be received in future/(1+r)^n, where r is the discounting rate and n is the year in which the cash flow will happen.
In this case the initial cash outlay in time period 0 is $200,000. The future cash flows for the periods 1 to 5 (in case of strong market) is $80,000 each year. Further the machine will be sold for $1,000 at the end of the 5th period.
Present value of these future cash flows = 80,000/(1+r)^1 + 80,000/(1+r)^2 + 80,000/(1+r)^3 + 80,000/(1+r)^4 + 80,000/(1+r)^5 + 1,000/(1+r)^5.
The machine should be purchased only if 80,000/(1+r)^1 + 80,000/(1+r)^2 + 80,000/(1+r)^3 + 80,000/(1+r)^4 + 80,000/(1+r)^5 + 1,000/(1+r)^5 > 200,000. In other words the machine should be purchased only if the sum of all discounted values of future revenue > the initial outlay of 200,000.
In case of a weak market the revenue per year is $30,000 and total revenue generated is $30,000*5 = $150,000. Even without discounting the revenue stream in case of a weak market we can see that the revenues ($150,000) are less than the initial outlay of $200,000.
Thus the purchase of machine should be avoided in case there are high chances of a weak market.
Another possibility is that there is a different probability for each market i.e. 0.80 for a strong market and 0.20 for a weak market or 0.20 for a strong market and 0.80 for a weak market. Probable cash flow = probability of strong market*revenue + probability of weak market*revenue. So, if probability for strong market is 0.80 and for weak market is 0.20 then the probable revenue = 0.80*80,000 + 0.20*30,000 = 64,000+6,000 = 70,000.
If chances of a weak market are 0.80 and that for a strong market is 0.20 then probable revenue is 0.80*30,000 + 0.20*80,000 = 24,000+16,000 = 40,000.
To make my decision I will need to additional pieces of information – (i) the discounting rate (ii) probability of occurring of each of the two economic conditions.
It is only with these pieces of information I will be able to make a proper and prudent decision. But on the face of it investment in the new machine should be avoided if the market is expected to remain weak for the entire duration of period 1 to period 5.
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