Question

12.       You have negotiated to buy a local small business for $200,000 that you estimate will provide you net income (or net cash flow) of approximately $65,000 per year (after all cash costs and expenses) for the “foreseeable future.” What is the “Present Value” of this company based on its expected cash flows, assuming no significant growth in income, and assuming your required rate of return (or discount rate) is 25.0%?

13.       Using the scenario above, what would your monthly payment be if you put 50% (or $100,000) down to purchase the business, and financed the balance over 5 years at a borrowing rate of 7.0%? With the resulting payment, what would your estimated annual net income be?

14.       You win a $1.2 million lottery. You will receive equal monthly payments of $5,000 for 20 years. Your discount rate is 8.0%. What is the "Present Value" of your lottery winnings?

15.       You purchased your home 35 years ago (in 1979) in sunny Southern California. You paid $60,000 for the home then. Based on comparables in the area, the home is now worth approximately $900,000. What is your compound annual rate of return on the home?

Answer 1

12)

Net income (or net cash flow) = $65,000 per year

Rate of return (or discount rate) = 25.0%

Present Value of Company based on cashflow = Net income / Rate of return

Present Value of Company based on cashflow = $65,000 / 25%

Present Value of Company based on cashflow = $260,000

13)

Loan Amount = $100,000

Interest rate = 7%

No of periods = 5 years * 12 = 60 months

Monthly payment = (Monthly interest rate / 1 - (1 + Monthly interest rate)^{- no of periods} ) * Loan Amount

Monthly payment = ((7% / 12) / (1 - (1 + (7% / 12))^-60)) * $100,000

Monthly payment = $1980.12

Net income after Monthly payment = Net Income - (12 * Monthly payment)

Net income after Monthly payment = $65,000 - (12 * $1980.12)

Net income after Monthly payment = $41,238.56

14)

Monthly payment = $5000

Discount rate = 8%

No of periods = 20 years * 12 = 240 months

Present Value of your lottery winnings = Monthly payment / (1 + Monthly Discount rate)^period +...+Monthly payment / (1 + Monthly Discount rate)^period

Using the PVIFA formula to value the monthly payments = (1 - (1 + Interest rate)^{- no of periods} ) / Interest rate

Present Value of your lottery winnings = (1 - (1 + Monthly Discount rate)^{- no of periods} ) / Monthly Discount rate * Monthly payment

Present Value of your lottery winnings = (1 - (1 + (8% / 12))^-240) / (8% / 12) * $5000

Present Value of your lottery winnings = $597,771.46

15)

Home Value 35 years ago = $60,000

Home Value Today = $900,000

No of periods = 35 years

Home Value Today = Home Value 35 years ago * (1 + compound annual rate)^{no of periods}

$900,000 = $60,000 * (1 + compound annual rate)³⁵

$900,000 / $60,000 = (1 + compound annual rate)³⁵

15 = (1 + compound annual rate)³⁵

(1 + compound annual rate) = (15)^(1/35)

(1 + compound annual rate) = 1.080445

Compound annual rate = 0.080445 or 8.0445%