Part One: Present Value Problems

1. Suppose you invest $2,500 in an account bearing interest at the rate of 14% per year. What will the future value of your investment in six years? FV = PV x (1 + interest rate)^n FV = 2,500 x (1 + .14)^6
FV = 2,500 x (1.14)^6
FV = 2,500 x 1.14 x 1.14 x 1.14 x 1.14 x 1.14 x 1.14
FV = $5487.43

2. Your best friend won the Wheel of Fortune in Las Vegas and has offered to give you $10,000 in five years, after he has collected his first million dollars. If you consider that if you had the money in your hand today, you would be able to get 12% annual interest, what is the present value of the gift?

PV = FV/(1 + interest rate)^ n
PV = 10,000/(1 + .12)^5
PV = 10,000/(1.12)^5
PV = 10,000/1.12 x 1.12 x 1.12 x 1.12 x 1.12
PV = 10,000/1.76
PV = $5,681.82

FV = PV x (1 + interest rate)^n
FV = 10,000 x (1 + .12)^5
FV = 10,000 x (1.12)^5
FV = 10,000 x (1.12 x 1.12 x 1.12 x 1.12 x 1.12)
FV = 10,000 x (1.76)
FV = $17,600

3. In four years, you would like to purchase a villa in the Alps. You estimate that the property will cost you $52,500 when you are ready to buy. How much money would you need to invest each year at 6% interest so that you would have the $52,500? PV = FV/(1 + interest rate)^ n PV = 52,500/(1 + .06)^4 PV = 52,500/(1.06)^4 PV = 52,500/1.06 x 1.06 x 1.06 x 1.06 PV = 52,500/ 1.26 PV = $41,666.66 (investing $41,667 would give you $52,500.42 in 4 years with the 6% interest rate. Investing the $41,666.66 would give you $52,499.99. It would be wiser to be 42 cents over than one penny short)

4. You have estimated that you will need $13,000 to complete your degree in three years. How much money do you need in your account at this moment to be able to cover the expense? Your account bears interest at 10% per year. PV = FV/(1 + interest rate)^ n PV = 13,000 / (1 + 0.10)^3 PV = 13,000 / (1.1)^3 PV = 13,000 / (1.1 x 1.1 x 1.1) PV = 13,000 / 1.331 PV = $9,767.09 (investing $9,800 would give you $13,043.80 in 3 years with the interest rate of 10% per year. Investing the $9,767.09 would give you $12,999.99. It would be wiser to have $43.80 more than to be one penny short)

Part Two: Contribution Margin Problems

Scenario: You have decided to open a pizza parlor in your hometown. You plan to deliver your pizzas in a four mile radius from your shop. Your annual fixed expenses are $54,000. You charge $10 for a pizza and it costs you $6 to make and deliver each pizza. Do not calculate income taxes for the purpose of this exercise.

Complete the following problems:
1. Using the contribution-margin approach, what is your break-even point in pizzas? QBE = [FC / (P – VC)] OBE = [54,000 / (10 – 6)]
QBE = [54,000 / 4]
QBE = 13,500 pizzas must be sold to break even

2. What is the contribution-margin ratio? The ratio is the unit contribution margin divided by the unit sales price. Ratio = ($10 - $6) / $10 per pizza Ratio = 4/10 = .4

3. Compute the break-even sales ratio using the contribution-margin ratio in your calculations. Ratio = fixed costs / CM ratio Break even sales = $54,000 / .4 = $135,000

4. Compute the number of pizzas that must be sold to earn a net profit of $60,000. To earn a net profit of $60,000, the pizza parlor must sell 28,500 pizzas.
Z = number of pizzas needed to meet $60,000 net profit
Z = FC + net profit / (P – VC)
Z = 54,000 + 60,000 / 4
Z = 28,500 pizzas