1. **State the problem:** A firm can either purchase a machine for 20000 or lease it for 8000 in the first year, with the lease payment decreasing by 1000 each subsequent year for 4 years. We want to find the present value of the lease payments given a 15% interest rate. 2. **Formula and explanation:** The present value (PV) of a series of payments is calculated by discounting each payment to its present value using the formula: $$PV = \sum_{t=1}^n \frac{R_t}{(1+i)^t}$$ where $R_t$ is the payment at year $t$, $i$ is the interest rate (0.15), and $n$ is the number of years (4). 3. **List the lease payments:** Year 1: 8000 Year 2: 7000 Year 3: 6000 Year 4: 5000 4. **Calculate present value of each payment:** $$PV = \frac{8000}{(1+0.15)^1} + \frac{7000}{(1+0.15)^2} + \frac{6000}{(1+0.15)^3} + \frac{5000}{(1+0.15)^4}$$ 5. **Calculate each term:** $$\frac{8000}{1.15} = 6956.52$$ $$\frac{7000}{1.15^2} = \frac{7000}{1.3225} = 5290.20$$ $$\frac{6000}{1.15^3} = \frac{6000}{1.5209} = 3943.40$$ $$\frac{5000}{1.15^4} = \frac{5000}{1.7490} = 2859.73$$ 6. **Sum the present values:** $$PV = 6956.52 + 5290.20 + 3943.40 + 2859.73 = 19049.85$$ **Final answer:** The present value of renting the machine is approximately **19049.85**.