Question

both ideas require a $12,500 investment today (T-o 6), while Investment B will grow to $25,000 at the ou are trying to compare two six year investment ideoas, Investment A will grow to $50,000 at the end of year 6 (T- end of year 6-6). Estimate the annualized return for each investment using the Rule of 72. Next, find the Compound Anmual Growth Rate (i.e. geometric average) for each investment, which we learned is more precise that the Rule of 72. You can use the timeline below to help answer problems 1-2 $ 50,000 25,000 YEAR 12,500 $ (12.500 1. The Rule ot 72 estimates the return on Investment A will be closest to a. 12.0% per year b. 12.2% per year c. 24.0% per year d. 26.0% per year e. 50.0% per year 2. Compare the Rule of 72 to the CAGRs for each investment. Based on your observations, which of the following stotements is most accurate a. The Rule of 72 does a better ¡ob of estimating the annualized return of Investment LhoninvestmentA; The Rule of 72 ynderestimates the octual return on Investment & by 2.0 b. The Rule of 72 does a better job of estimating the onnualized return of Investment A thon Investment The Rule of 72 overestimates the actual return on hwmentA by 20h c. The Rule of 72 does a better job of estimating the annualized return of Investment &than Investment A The Rule of 72 grerestimates the actual return on Investment & by Q.2 d. The Rule of 72 does a better İob of estimating the anualized return of Investment Athan Investment The Rule of 72 overestimates the octual return on InvestmentA by The Rule of 72 does a better İob of estimating the annualized return of Investment B thon bes mentAu 29s e. The Rule of 72 underestimates the octo' return on Investment by 20% Assume a discount rate of 10.0% per year. Using the concept of discount factors to compare receiving 20 today (T-O) to receiving $20 20 years from now (T-20). Which of the following stotements is the 3. most accurate The $20 received 20 years from now is worth only 5% of the value today a, b, The $20 received 20 years from now is worth only 10% of the value today The $20 received 20 years from now is worth only 15% of the value today c. d. The $20 received 20 years from now is worth only $4 today e. The $20 received 20 years from now is worth only $6 today 4. In the 5-Stage DuPont ROE formula, which of the following stages is considered to be a relative measurement of how much long term debt there is on the balance sheet (ie. a solvency ratio) a. NI/ SE, or the return on equity b. NI/Sales, or the profit margin c. EBIT /Sales, or the operating margin d. EBIT Interest, or the times interest earned ratio e. TA/SE or the leverage ratio

Answer 1

Question 1:

The rule of 72 follows compound interest curve. For example, if an investment grows to twice of initial investment at the end of 2 years , it will grow to 4 times of initial investment at the end of 4 years (i.e, 2*2)  and similarly 8 times initial investment at the end of 6 years ( i.e., 2*3).  

For investment A, the principal investment of $12,500 grows to $50,000 at the end of 6 years. Thus, the initial investment grows to 4 times the initial investment at the end of 6 years. Thus, as per compound interest curve, investment would grow to twice of initial investment at the end of 3 years. The 72 rule says: time (T) to double investment = 72 / R (rate of interest).

Here, T = 3 years.

$3=72/R$

$R=72/3$

$R=24$%

Question 2:

As per CAGR rule: Final amount=A; Initial investment =P; Time=T; Rate of interest =R

$A=P(1+R/100)^T$

	Investment A	Investment B
CAGR	$50000=12500(1+R/100)^6$ R=26%	$25000=12500(1+R/100)^6$ R=12.25%
72 Rule	$R=72/3$ R=24%	$R=72/6$ R=12%

Thus, Answer is option E. The rule of 72 does a better job of estimating the rate of return of investment B than A. &2 rule, underestimates the rate o return on Investment A by 2%.

Question 3:

As per CAGR (Compound Annual Growth Rate):

$A=P(1+R/100)^T$

Here, T=20; A=20$, R=10%

20=P(1+10/100)²⁰

P= $1.05 which is 5% of $20.

Thus answer is option A.

Question 4:

Answer is option e. As leverage ratio gives an indication of how the company's assets and business operations are financed (debt or equity). Common leverage ratios are Debt/Equity ratio, Debt//Capital Ratio and Debt/Total Asset ratio.