1. **Problem Statement:** Molecugen forecasts sales of 5,000 units in year 1, decreasing by 10% annually for 5 years. Sales price is 15 per unit, operating cost is 5 per unit, general expenses are 15,000 per year, initial investment is 20,000 (land 10,000 + setup 10,000), straight-line depreciation over 5 years, tax rate 35%, cost of capital 10%. Determine if the project is acceptable. 2. **Formulas and Rules:** - Demand each year: $D_t = D_1 \times (1 - 0.10)^{t-1}$ for $t=1,...,5$ - Revenue: $R_t = D_t \times 15$ - Operating cost: $OC_t = D_t \times 5$ - Depreciation: $Dep = \frac{20,000}{5} = 4,000$ per year - Earnings before tax (EBT): $EBT_t = R_t - OC_t - 15,000 - Dep$ - Tax: $Tax_t = 0.35 \times EBT_t$ if $EBT_t > 0$, else 0 - Net income: $NI_t = EBT_t - Tax_t$ - Cash flow: $CF_t = NI_t + Dep$ - Initial investment: $-20,000$ - Use Net Present Value (NPV) to decide acceptability: $$NPV = -20,000 + \sum_{t=1}^5 \frac{CF_t}{(1+0.10)^t}$$ If $NPV \geq 0$, project is acceptable. 3. **Calculate demand each year:** $D_1 = 5,000$ $D_2 = 5,000 \times 0.9 = 4,500$ $D_3 = 4,500 \times 0.9 = 4,050$ $D_4 = 4,050 \times 0.9 = 3,645$ $D_5 = 3,645 \times 0.9 = 3,280.5$ 4. **Calculate revenue and operating cost each year:** $R_t = D_t \times 15$ $OC_t = D_t \times 5$ | Year | Demand | Revenue ($R_t$) | Operating Cost ($OC_t$) | |---|---|---|---| | 1 | 5,000 | 75,000 | 25,000 | | 2 | 4,500 | 67,500 | 22,500 | | 3 | 4,050 | 60,750 | 20,250 | | 4 | 3,645 | 54,675 | 18,225 | | 5 | 3,280.5 | 49,207.5 | 16,402.5 | 5. **Calculate Earnings Before Tax (EBT):** $EBT_t = R_t - OC_t - 15,000 - 4,000$ | Year | $EBT_t$ | |---|---| | 1 | 75,000 - 25,000 - 15,000 - 4,000 = 31,000 | | 2 | 67,500 - 22,500 - 15,000 - 4,000 = 26,000 | | 3 | 60,750 - 20,250 - 15,000 - 4,000 = 21,500 | | 4 | 54,675 - 18,225 - 15,000 - 4,000 = 17,450 | | 5 | 49,207.5 - 16,402.5 - 15,000 - 4,000 = 13,805 | 6. **Calculate Tax and Net Income:** $Tax_t = 0.35 \times EBT_t$ $NI_t = EBT_t - Tax_t$ | Year | Tax | Net Income ($NI_t$) | |---|---|---| | 1 | 10,850 | 20,150 | | 2 | 9,100 | 16,900 | | 3 | 7,525 | 13,975 | | 4 | 6,107.5 | 11,342.5 | | 5 | 4,831.75 | 8,973.25 | 7. **Calculate Cash Flow:** $CF_t = NI_t + Dep = NI_t + 4,000$ | Year | Cash Flow ($CF_t$) | |---|---| | 1 | 24,150 | | 2 | 20,900 | | 3 | 17,975 | | 4 | 15,342.5 | | 5 | 12,973.25 | 8. **Calculate NPV:** $$NPV = -20,000 + \sum_{t=1}^5 \frac{CF_t}{(1.10)^t}$$ Calculate each term: $\frac{24,150}{1.10} = 21,954.55$ $\frac{20,900}{1.10^2} = 17,256.20$ $\frac{17,975}{1.10^3} = 13,489.15$ $\frac{15,342.5}{1.10^4} = 10,474.15$ $\frac{12,973.25}{1.10^5} = 8,052.10$ Sum of discounted cash flows = 21,954.55 + 17,256.20 + 13,489.15 + 10,474.15 + 8,052.10 = 71,226.15 $NPV = -20,000 + 71,226.15 = 51,226.15$ 9. **Conclusion:** Since $NPV > 0$, the project is acceptable at a 10% cost of capital.