Internal Rate of Return worksheet

1. Internal rate of return (per quarter): 9.93%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,250.00}}{{\left(1+0.09931452\right)}^1}+\frac{\mathrm{\$3,600.00}}{{\left(1+0.09931452\right)}^2}+\frac{\mathrm{\$5,400.00}}{{\left(1+0.09931452\right)}^3}-\mathrm{\$10,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per quarter

   $\text{IRR}$$=\mathrm{9.9315\%}$

4. Turn it into a yearly rate. Let it compound (grow on top of itself) over 4 quarters

   ${\left(1+0.09931452\right)}^4-1$$=\mathrm{46.0454\%}$

2. Internal rate of return (per quarter): 29.08%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,200.00}}{{\left(1+0.29078234\right)}^1}+\frac{\mathrm{\$5,000.00}}{{\left(1+0.29078234\right)}^2}+\frac{\mathrm{\$8,000.00}}{{\left(1+0.29078234\right)}^3}-\mathrm{\$9,200.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per quarter

   $\text{IRR}$$=\mathrm{29.0782\%}$

4. Turn it into a yearly rate. Let it compound (grow on top of itself) over 4 quarters

   ${\left(1+0.29078234\right)}^4-1$$=\mathrm{177.5953\%}$

3. Internal rate of return (per year): 23.32%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,000.00}}{{\left(1+0.23318968\right)}^1}+\frac{\mathrm{\$3,500.00}}{{\left(1+0.23318968\right)}^2}+\frac{\mathrm{\$8,000.00}}{{\left(1+0.23318968\right)}^3}-\mathrm{\$9,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per year

   $\text{IRR}$$=\mathrm{23.319\%}$

4. Internal rate of return (per year): 0%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,000.00}}{{\left(1+0\right)}^1}+\frac{\mathrm{\$4,200.00}}{{\left(1+0\right)}^2}+\frac{\mathrm{\$6,800.00}}{{\left(1+0\right)}^3}-\mathrm{\$14,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per year

   $\text{IRR}$$=\mathrm{0\%}$

5. Internal rate of return (per month): 29.23%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$4,000.00}}{{\left(1+0.29233353\right)}^1}+\frac{\mathrm{\$4,600.00}}{{\left(1+0.29233353\right)}^2}+\frac{\mathrm{\$6,800.00}}{{\left(1+0.29233353\right)}^3}-\mathrm{\$9,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per month

   $\text{IRR}$$=\mathrm{29.2334\%}$

4. Turn it into a yearly rate. Let it compound (grow on top of itself) over 12 months

   ${\left(1+0.29233353\right)}^{12}-1$$=\mathrm{2,070.1781\%}$

6. Internal rate of return (per quarter): 18.67%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,500.00}}{{\left(1+0.18674218\right)}^1}+\frac{\mathrm{\$4,200.00}}{{\left(1+0.18674218\right)}^2}+\frac{\mathrm{\$6,800.00}}{{\left(1+0.18674218\right)}^3}-\mathrm{\$10,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per quarter

   $\text{IRR}$$=\mathrm{18.6742\%}$

4. Turn it into a yearly rate. Let it compound (grow on top of itself) over 4 quarters

   ${\left(1+0.18674218\right)}^4-1$$=\mathrm{98.3469\%}$

7. Internal rate of return (per year): 23.16%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$2,750.00}}{{\left(1+0.23159996\right)}^1}+\frac{\mathrm{\$5,500.00}}{{\left(1+0.23159996\right)}^2}+\frac{\mathrm{\$4,000.00}}{{\left(1+0.23159996\right)}^3}-\mathrm{\$8,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per year

   $\text{IRR}$$=\mathrm{23.16\%}$

8. Internal rate of return (per year): 13.77%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,000.00}}{{\left(1+0.13767237\right)}^1}+\frac{\mathrm{\$4,200.00}}{{\left(1+0.13767237\right)}^2}+\frac{\mathrm{\$6,800.00}}{{\left(1+0.13767237\right)}^3}-\mathrm{\$10,500.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per year

   $\text{IRR}$$=\mathrm{13.7672\%}$

9. Internal rate of return (per month): 25.67%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$3,200.00}}{{\left(1+0.256681\right)}^1}+\frac{\mathrm{\$5,500.00}}{{\left(1+0.256681\right)}^2}+\frac{\mathrm{\$5,400.00}}{{\left(1+0.256681\right)}^3}-\mathrm{\$8,750.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per month

   $\text{IRR}$$=\mathrm{25.6681\%}$

4. Turn it into a yearly rate. Let it compound (grow on top of itself) over 12 months

   ${\left(1+0.256681\right)}^{12}-1$$=\mathrm{1,451.3171\%}$

10. Internal rate of return (per year): 6.75%

1. Look for the rate r where the marked-down cash flows add up to exactly your investment, so the NPV is zero. The flows switch sign 1 time, so there can be at most 1 such rate

   $\text{NPV(r)}$$=\text{−I + Σ CFₖ ÷ (1 + r)^k}$$=0$

2. No formula gives r directly, so search for it. Find two rates where the NPV switches sign, then close in between them until the NPV is zero

   $\frac{\mathrm{\$2,700.00}}{{\left(1+0.06747077\right)}^1}+\frac{\mathrm{\$4,000.00}}{{\left(1+0.06747077\right)}^2}+\frac{\mathrm{\$7,250.00}}{{\left(1+0.06747077\right)}^3}-\mathrm{\$12,000.00}$$=\mathrm{\$0.00}$

3. The rate that does this, as a percent per year

   $\text{IRR}$$=\mathrm{6.7471\%}$