Financial Calculations: DSO, ROA, ROE, and More
Financial Calculations
1. Baker Brothers’ Days Sales Outstanding and Cash Freed Up
Question: Baker Brothers has accounts receivable of $700,000 and sales of $2,000,000. What is Baker’s days sales outstanding? How much cash would Baker Brothers free up if it reduced its days sales outstanding to 45 days?
Solution:
DSO = (Accounts Receivable / Sales) * 365
DSO = (700,000 / 2,000,000) * 365 = 128 days
Cash Freed Up = (128 days – 45 days) * (2,000,000 / 365) = $454,794.35
2. Debt Ratio from Equity Multiplier
Question: A firm that has an equity multiplier of 5.0 will have a debt ratio of what?
Solution:
Debt Ratio (DR) = 1 – (1 / Equity Multiplier)
DR = 1 – (1 / 5) = 1 – 0.2 = 0.8 or 80%
3. Doublewide Dealers’ Asset Turnover and Equity Multiplier
Question: Doublewide Dealers has an ROA of 14 percent, a 4 percent profit margin, and a return on equity equal to 15 percent. What is the company’s total assets turnover? What is the firm’s equity multiplier?
Solution:
ROA = Profit Margin (PM) * Total Asset Turnover (TATO)
14% = 4% * TATO
TATO = 3.5
ROE = PM * TATO * Equity Multiplier (EM)
15% = 4% * 3.5 * EM
EM = 1.07
4. Royce Corp’s Profit Margin
Question: Royce Corp’s sales last year were $350,000, and its net income was $48,000. What was its profit margin?
Solution:
Profit Margin (PM) = Net Income / Sales
PM = 48,000 / 350,000 = 13.7%
5. Song Corp’s P/E Ratio
Question: Song Corp’s stock price at the end of last year was $25.00 and its earnings per share for the year were $2.00. What was its P/E ratio?
Solution:
P/E Ratio = Stock Price / Earnings Per Share
P/E = 25 / 2 = 12.5x
6. Future Value of a Deposit
Question: If you deposit $5,000 in an account that pays 10% interest annually, how much will be in your account after 15 years?
Solution:
Using a financial calculator or spreadsheet:
N = 15, PV = -5,000, I/Y = 10, PMT = 0
FV = $20,886.24
7. Present Value of a Future Amount
Question: What is the present value of $25,000 in 12 years if the interest rate is 9% annually?
Solution:
Using a financial calculator or spreadsheet:
N = 12, I/Y = 9, PMT = 0, FV = 25,000
PV = -$8,888.37
8. Required Interest Rate for Retirement
Question: Your parents will retire in 25 years. They currently have $75,000, and they think they will need $300,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?
Solution:
Using a financial calculator or spreadsheet:
N = 25, PV = -75,000, PMT = 0, FV = 300,000
I/Y = 5.7%
9. Future Value of an Ordinary Annuity and Annuity Due
Question: What is the future value of an 8%, 12-year ordinary annuity that pays $15,000 each year? If this was an annuity due, what would its future value be?
Solution:
Ordinary Annuity:
Using a financial calculator or spreadsheet:
N = 12, I/Y = 8, PV = 0, PMT = -15,000
FV = $284,656.90
Annuity Due:
FV (Annuity Due) = FV (Ordinary Annuity) * (1 + Interest Rate)
FV (Annuity Due) = $284,656.90 * (1 + 0.08) = $307,429.45
10. Present Value of an Ordinary Annuity and Annuity Due
Question: What is the present value of a 7%, 15-year ordinary annuity that pays $25,000 each year? If this was an annuity due, what would its present value be?
Solution:
Ordinary Annuity:
Using a financial calculator or spreadsheet:
N = 15, I/Y = 7, PMT = -25,000, FV = 0
PV = $227,697.85
Annuity Due:
PV (Annuity Due) = PV (Ordinary Annuity) * (1 + Interest Rate)
PV (Annuity Due) = $227,697.85 * (1 + 0.07) = $243,636.70
11. Present Value of Uneven Cash Flows
Question: An investment will pay $200 at the end of the first year, $250 at the end of years 2 and 3, and $300 at the end of year 4. If other investments of equal risk earn 8 percent annually, what is its present value?
Solution:
Using a financial calculator or spreadsheet (Cash Flow function):
CF0 = 0, CF1 = 200, CF2 = 250, CF3 = 250, CF4 = 300, I/Y = 8
NPV = $801.85
12. Monthly Loan Payment
Question: You want to buy a car and have to finance $25,000. The loan will be fully amortized over 5 years and the nominal interest rate will be 5% with interest and payments paid monthly. What will be the monthly loan payment?
Solution:
Using a financial calculator or spreadsheet:
N = 60 (5 years * 12 months), I/Y = 0.4167 (5% / 12), PV = 25,000, FV = 0
PMT = -$471.79
13. Effective Interest Rate with Daily Compounding
Question: When you apply for a credit card, you read that the annual interest rate is 18%. However, the fine print at the bottom of your monthly statement says that the interest compounds daily. What is the effective interest rate (the real rate you are paying)?
Solution:
Using a financial calculator or spreadsheet:
NOM = 18, C/Y = 365
EFF = 19.72%
14. Effective Interest Rate with Quarterly Compounding
Question: Your bank account pays a 6% nominal interest rate that is compounded quarterly. What is the effective interest rate?
Solution:
Using a financial calculator or spreadsheet:
NOM = 6, C/Y = 4
EFF = 6.14%
15. Future Value of an Annuity Due
Question: What is the future value of an annuity due with 20 payments of $6,000 at a 7% interest rate?
Solution:
Using a financial calculator or spreadsheet (set to BEGIN mode for annuity due):
N = 20, I/Y = 7, PMT = -6,000, PV = 0
FV = $263,191.06
16. Present Value of an Ordinary Annuity
Question: What is the present value of an ordinary annuity with 10 payments of $4,100 at a 5.5% interest rate?
Solution:
Using a financial calculator or spreadsheet:
N = 10, I/Y = 5.5, PMT = -4,100, FV = 0
PV = $30,094.27
17. Required Interest Rate for Future Value
Question: What interest rate must you earn if you currently have $10,000 and want $30,000 in 10 years?
Solution:
Using a financial calculator or spreadsheet:
N = 10, PV = -10,000, PMT = 0, FV = 30,000
I/Y = 11.61%
18. Time to Reach a Future Value
Question: If you invest $5,000 today at a 7% interest rate compounded annually, how many years will it take for your investment to double?
Solution:
Using the Rule of 72 (an approximation):
Years to Double ≈ 72 / Interest Rate
Years to Double ≈ 72 / 7 ≈ 10.3 years
Using a financial calculator or spreadsheet:
PV = -5,000, FV = 10,000, I/Y = 7, PMT = 0
N ≈ 10.24 years