A contractor invests $190,000 in equipment that returns $39,000 per year for 10 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 20% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 10) = P/A = 190000/39000 = 4.8718$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-10]/i = 4.8718 is i = 15.79$$

4. After-tax cash flow — A_at = A(1 − t) = $39,000(1 − 0.20) = $31,200

5. After-tax (P/A) required — 6.0897

6. Solve again — i_at ≈ 10.21%

Why the other options are there

• 105.3% (simple total return)
• 20.5% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $87,000 in equipment that returns $18,000 per year for 8 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 35% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 8) = P/A = 87000/18000 = 4.8333$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-8]/i = 4.8333 is i = 12.79$$

4. After-tax cash flow — A_at = A(1 − t) = $18,000(1 − 0.35) = $11,700

5. After-tax (P/A) required — 7.4359

6. Solve again — i_at ≈ 1.65%

Why the other options are there

• 65.5% (simple total return)
• 20.7% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $60,000 in equipment that returns $29,000 per year for 5 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 25% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 5) = P/A = 60000/29000 = 2.0690$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-5]/i = 2.0690 is i = 39.03$$

4. After-tax cash flow — A_at = A(1 − t) = $29,000(1 − 0.25) = $21,750

5. After-tax (P/A) required — 2.7586

6. Solve again — i_at ≈ 23.77%

Why the other options are there

• 141.7% (simple total return)
• 48.3% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $111,000 in equipment that returns $34,000 per year for 10 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 25% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 10) = P/A = 111000/34000 = 3.2647$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-10]/i = 3.2647 is i = 28.05$$

4. After-tax cash flow — A_at = A(1 − t) = $34,000(1 − 0.25) = $25,500

5. After-tax (P/A) required — 4.3529

6. Solve again — i_at ≈ 18.91%

Why the other options are there

• 206.3% (simple total return)
• 30.6% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $125,000 in equipment that returns $8,000 per year for 5 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 22% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 5) = P/A = 125000/8000 = 15.6250$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-5]/i = 15.6250 is i = 0.01$$

4. After-tax cash flow — A_at = A(1 − t) = $8,000(1 − 0.22) = $6,240

5. After-tax (P/A) required — 20.0321

6. Solve again — i_at ≈ 0.01%

Why the other options are there

• -68.0% (simple total return)
• 6.4% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $46,000 in equipment that returns $35,000 per year for 8 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 21% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 8) = P/A = 46000/35000 = 1.3143$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-8]/i = 1.3143 is i = 75.23$$

4. After-tax cash flow — A_at = A(1 − t) = $35,000(1 − 0.21) = $27,650

5. After-tax (P/A) required — 1.6637

6. Solve again — i_at ≈ 58.61%

Why the other options are there

• 508.7% (simple total return)
• 76.1% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $173,000 in equipment that returns $13,000 per year for 5 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 23% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 5) = P/A = 173000/13000 = 13.3077$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-5]/i = 13.3077 is i = 0.01$$

4. After-tax cash flow — A_at = A(1 − t) = $13,000(1 − 0.23) = $10,010

5. After-tax (P/A) required — 17.2827

6. Solve again — i_at ≈ 0.01%

Why the other options are there

• -62.4% (simple total return)
• 7.5% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $176,000 in equipment that returns $28,000 per year for 10 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 22% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 10) = P/A = 176000/28000 = 6.2857$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-10]/i = 6.2857 is i = 9.47$$

4. After-tax cash flow — A_at = A(1 − t) = $28,000(1 − 0.22) = $21,840

5. After-tax (P/A) required — 8.0586

6. Solve again — i_at ≈ 4.13%

Why the other options are there

• 59.1% (simple total return)
• 15.9% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $160,000 in equipment that returns $33,000 per year for 5 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 32% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 5) = P/A = 160000/33000 = 4.8485$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-5]/i = 4.8485 is i = 1.03$$

4. After-tax cash flow — A_at = A(1 − t) = $33,000(1 − 0.32) = $22,440

5. After-tax (P/A) required — 7.1301

6. Solve again — i_at ≈ 0.01%

Why the other options are there

• 3.1% (simple total return)
• 20.6% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation

A contractor invests $160,000 in equipment that returns $14,000 per year for 5 years with no salvage. Determine the rate of return, and estimate the after-tax return at a 29% tax rate on the net income.

Start with the thinking

• The rate of return is the interest rate that makes present worth zero — solved by trial or by the calculator's IRR.
• A quick after-tax screen scales the annual return by (1 − tax rate) and re-solves.

Step-by-step solution

1. Formula

   $$0 = -P + A(P/A, i, n)$$

2. Set up

   $$(P/A, i, 5) = P/A = 160000/14000 = 11.4286$$

3. Solve for i

   $$the rate satisfying [1 - (1+i)^-5]/i = 11.4286 is i = 0.01$$

4. After-tax cash flow — A_at = A(1 − t) = $14,000(1 − 0.29) = $9,940

5. After-tax (P/A) required — 16.0966

6. Solve again — i_at ≈ 0.01%

Why the other options are there

• -56.3% (simple total return)
• 8.8% (ignored the time value of money)

Reference: FE Reference Handbook — Engineering Economics → Taxation