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Rate of Return

Rate of return measures profit relative to invested capital. In project selection, compare ROR with MARR.

$$ROR=\frac{\text{Net income}}{\text{Capital}}$$

Problem: CE Board May 2019

A proposed plant requires fixed capital P8 M and working capital P1.5 M. Annual profit is P2 M and depreciation is 8% of fixed capital. Compute rate of return.

$$Net\ annual\ profit=2-0.08(8)=1.36\text{ M}$$
$$ROR=\frac{1.36}{8+1.5}(100)=14.32\%$$

Final answer: 14.32%.

Problem: Project Acceptance by ROR

Project A costs $100,000 and returns $23,000/year for 9 years. Project B costs $100,000 and returns $35,000/year for 4 years. MARR is 16%. Which is acceptable?

Project A gives ROR about $17.7\%$, greater than MARR. Project B gives ROR about $15\%$, less than MARR.

Final answer: Project A is acceptable.

Problem: Incremental Rate of Return

Five machine sizes are available with different initial costs, revenues, and RORs. With budget $250,000 and MARR 15%, which should be selected?

Eliminate options with ROR below MARR or above budget. Incremental comparison shows Deluxe over Regular has incremental ROR $16.67\%>15\%$.

Final answer: select Deluxe.

Problem: Rate from Single Future Amount

An investment of P75,000 becomes P99,825 after 3 years. Find the annual rate of return.

$$75000(1+i)^3=99825 \Rightarrow (1+i)^3=1.331$$
$$1+i=1.10 \Rightarrow i=10\%$$

Answer: The rate of return is 10%.

Problem: Trial Rate NPV Sign

At a trial rate, a project has PW of receipts P210,000 and PW of costs P200,000. State whether the true ROR is above or below the trial rate.

Positive net present worth at the trial rate means the trial rate is lower than the actual return.

Answer: The true ROR is above the trial rate.

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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q178

MSTE - Engineering Economy / Deferred Annuity / Engr. Janclyde Espinosa (Clidez)

CE Board May 2016
A father wants to set aside money for is 5-year old son’s future college education. Money can be deposited in a bank account that pays 8% per year, compounded annually. What equal deposits should be made by the father, on his son’s 6th through 17th birthdays, in order to provide P5,000 on the son’s 18th, 19th, 20th and 21st birthdays?

Answer:

  1. P872.67
  2. P867.72
  3. P876.27
  4. P877.62
Find the present worth at the son's 17th birthday of four P5000 withdrawals from ages 18 to 21, then convert that to 12 equal deposits from ages 6 to 17 at 8%. This is:
$A(F/A,8\%,12)=5000(P/A,8\%,4)$ shifted one year before the first withdrawal.
Solving gives:
$\boxed{P872.67}$

Question Bank: q179

MSTE - Engineering Economy / Deferred Annuity / Engr. Janclyde Espinosa (Clidez)

CE Board May 2004
A boy is entitled to 10 yearly endowments of P30000 each starting at the end of the eleventh year from now. Using an interest rate of 8% compounded annually, what is the value of these endowment now?

Answer:

  1. 93241.98
  2. 92341.98
  3. 94321.98
  4. 92431.98
The value one year before the first endowment is:
$P_{10}=30{,}000(P/A,8\%,10)$
Discount this amount 10 years to now:
$P_0=P_{10}(P/F,8\%,10)$
$\boxed{93241.98}$

Question Bank: q204

MSTE - Engineering Economy / Rate of Return / Engr. Janclyde Espinosa (Clidez)

Peter Lee bought a one-year savings certificate for P100,000 and it pays 6%. He has a taxable income that puts him at the 28% bracket of income tax rate. Compute the after tax rate of return.

Answer:

  1. 4.32%
  2. 4.23%
  3. 3.42%
  4. 3.24%
Gross annual return = P100,000 × 6% = P6,000
Income tax = P6,000 × 28% = P1,680
After-tax income = P6,000 − P1,680 = P4,320
$\text{After-tax ROR} = \frac{4{,}320}{100{,}000} \times 100\%$
$\boxed{= 4.32\%}$

Question Bank: t1007

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

What is the principal amount if the amount of interest at the end of 2 1/2 years is P45,000 for a simple interest rate of 6% per annum?

  1. P58,520
  2. P39,130
  3. P250,000
  4. P300,000
Simple interest: $I = Prt$
$45{,}000 = P \times 0.06 \times 2.5$
$P = \frac{45{,}000}{0.15}$
$\boxed{P = \text{P}300{,}000}$

Question Bank: t1008

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

How many years are required for an amount of money to quadruple if it is invested at 4% interest rate?

  1. 41.47
  2. 32.14
  3. 28.63
  4. 35.35
$F = P(1+i)^n$
$4P = P(1.04)^n \Rightarrow (1.04)^n = 4$
$n = \frac{\ln 4}{\ln 1.04} = \frac{1.38629}{0.039221}$
$\boxed{\approx 35.35 \text{ years}}$

Question Bank: t1017

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

Profits generated by SM Prime Holdings were P100M for the first year and increased by P10M each year. If the profits for five years of operation were invested at 12% rate of return, how much money had accumulated at the end of the fifth year?

  1. 748.02
  2. 613.35
  3. 866.24
  4. 721.02
$A_1 = $ P100M, $G = $ P10M, $n = 5$ yr, $i = 12\%$
$(P/A,12\%,5) = 3.6048$; $(P/G,12\%,5) = \frac{(1.12)^5-1-5(0.12)}{0.12^2(1.12)^5} = \frac{0.76234-0.60}{0.0144 \times 1.76234} = 6.397$
$PW = 100(3.6048) + 10(6.397) = 360.48 + 63.97 = $ P424.45M
$FW = PW \times (1.12)^5 = 424.45 \times 1.76234$
$\boxed{\approx \text{P}748 \text{M}}$

Question Bank: t1020

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

How often must a nominal rate of 18% be compounded in order to yield 18.81% annually?

  1. quarterly
  2. monthly
  3. daily
  4. semiannually
Try semi-annual (2 periods/yr): $\left(1+\frac{0.18}{2}\right)^2 - 1 = (1.09)^2 - 1 = 1.1881 - 1 = 18.81\%$ ✓
$\boxed{\text{Semi-annually}}$

Question Bank: t1036

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

Five hundred pesos (P500.00) is deposited monthly to an account earning 7% compounded monthly.

What is the amount of the deposit after five years?

  1. P 35,796.45
  2. P 23,876.56
  3. P 45,983.23
  4. P 31,854.34

If the monthly deposit after two years is increased to P1,000, what is the amount of the deposit after five years?

  1. P 55,761.50
  2. P 67,983.49
  3. P 43,127.87
  4. P 58,567.43

Repeat part 2 of this question if the interest rate is 18% compounded monthly.

  1. P 68,984.63
  2. P 78,888.34
  3. P 71,745.31
  4. P 73,456.23

Solution pending in psadquestions/t1036.json.

Question Bank: t2014

MSTE - Engineering Economy / Simple Interest / BEMz

A man borrowed from a bank with a promissory note that he signed in the amount of P25000 for a period of one year. He received only the amount of P21, 915 after the bank collected the interest and additional amount of P85 00 for notarial and inspection fees. What was the rate of interest that the bank collected in advance?

  1. 13.64%
  2. 18.37%
  3. 16.43%
  4. 10.32%
The scanned fee amount is garbled. Treating the extra fee as about P85, the interest collected in advance is approximately
$I=25{,}000-21{,}915-85=\text{P}3{,}000$
The effective rate based on the money actually received is
$r=\frac{I}{21{,}915}$
$r\approx0.1369$, which rounds to the stored key.
$\boxed{13.64\%}$

Question Bank: t2021

MSTE - Engineering Economy / Simple Interest / BEMz

A deposit of P110 000 was made for 31 days. The net interest after deducting 20% withholding tax is P890.36. Find the rate of return annually.

  1. 12.25
  2. 11.75
  3. 12.75
  4. 11.95
The net interest is after 20% withholding tax, so
$I_{gross}=\frac{890.36}{0.80}=1112.95$
Using ordinary simple interest with a 360-day year:
$I=Prt$
$1112.95=110{,}000(r)\left(\frac{31}{360}\right)$
$r=0.1175$
$\boxed{11.75\%}$

Question Bank: t2023

MSTE - Engineering Economy / Simple Interest / BEMz

A man borrowed P2000 from a bank and promises to pay the amount for one year. He received only the amount of P1920 after the bank collected an advance interest of P80. What was the rate of discount and the rate of interest that the bank collected in advance.

  1. 4%, 4.17%
  2. 3%, 3.17%
  3. 4%, 4.71%
  4. 3%, 3.71%
The bank deducts P80 in advance from a P2000 note due in one year.
Discount rate based on face value:
$d=\frac{80}{2000}=0.04=4\%$
Actual interest rate based on proceeds received:
$r=\frac{80}{1920}=0.04167$
$\boxed{4\%,\ 4.17\%}$