5. The Cornballer, invented by George Bluth in the mid-1970s, is a device used to make cornballs. It sold for $29.95. Suppose that 10,000 Cornballers were sold in 1981; 11,000 in 1982; and sales increasing by 10% each year until it was last sold in 1990 (when it was made illegal). Assume an interest rate of 12% per year. Assume sales were made at EOY. What was the worth of these cash flows in 1980?

$2,469,143.07

Explanation:

Step 1: Calculation of sales value for each year

Since sales unit increased 10% (i.e. 0.1) each year, the calculation of sales unit from 1983 till 1990 will be the multiplication of the previous sales unit by 1.1 (i.e. 1 + 0.1 = 1.1). The sales value will then be calculated by multipying the unit by the unit price of $29.95 as follows

1981 Sales value =  10,000 × $29.95 = $299,500.00

1982 Sales value = 11,000 × $29.95 = $329,450.00

1983 Sales value = (11,000 × 1.1) × $29.95 = 12,100  × $29.95 = $362,395.00

1984 Sales value = (12,100 × 1.1) × $29.95 = 13,310  × $29.95 = $398,634.50

1985 Sales value = (13,310 × 1.1) × $29.95 = 14,641  × $29.95 =  $438,497.95  

1986 Sales value = (14,641 × 1.1) × $29.95 = 16,105  × $29.95 = $482,347.75

1987 Sales value = (16,105 × 1.1) × $29.95 = 17,716  × $29.95 = $530,582.52  

1988 Sales value = (17,716 × 1.1) × $29.95 = 19,487  × $29.95 = $583,640.77  

1989 Sales value = (19,487 × 1.1) × $29.95 = 21,436  × $29.95 = $642,004.85  

1990 Sales value = (21,436 × 1.1) × $29.95 = 23,579  × $29.95 = $706,205.33  Step 2: Calculation of 1980 present value (PV) of sales value for each year

To do this, we will use the interest rate of 12% (i.e. 0.12) as our discounting factor (r) to calculate the PV for each year using the discounting formula (1+r)^n, where n is the number of year. In this, 1981 will be year 1 which continues till year 10 which 1990 as follows:

1981 PV = $299,500.00 ÷ (1.12)^2 = $267,410.71

1982 PV = $329,450.00 ÷ (1.12)^2 = $262,635.52

1983 PV = $362,395.00 ÷ (1.12)^3 = $257,945.60  

1984 PV = $398,634.50 ÷ (1.12)^4 = $253,339.43  

1985 PV = $438,497.95 ÷ (1.12)^5 =  $248,815.51  

1986 PV = $482,347.75 ÷ (1.12)^6 = $244,372.38  

1987 PV = $530,582.52 ÷ (1.12)^7 = $240,008.59

1988 PV = $583,640.77 ÷ (1.12)^8 = $235,722.72

1989 PV = $642,004.85 ÷ (1.12)^9 = $231,513.38

1990 PV = $706,205.33 ÷ (1.12)^10 = $227,379.22  

Step 3: Calculation of the worth of these cash flows in 1980

The worth of all the cash flows in 1980 is the addition of all the PV calculated in step 2 above. And this is equal to $2,469,143.07.

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