Subjects finance

Investment Timing 90C114

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1. **Problem Statement:** Company F can invest now or delay investment by 1 year. We need to decide which option yields a higher Net Present Value (NPV). 2. **Given Data:** - Initial outlay now: 100,000 - Expected cash flows if invest now: 60,000 at Year 1, 80,000 at Year 2 - Expected cash flows if delay 1 year: 70,000 at Year 2, 90,000 at Year 3 - Discount rate: 10% (0.10) 3. **Formula for NPV:** $$\text{NPV} = \sum_{t=1}^n \frac{CF_t}{(1+r)^t} - \text{Initial Outlay}$$ where $CF_t$ is cash flow at year $t$, $r$ is discount rate. 4. **Calculate NPV if invest now:** $$\text{NPV}_{now} = -100,000 + \frac{60,000}{(1+0.10)^1} + \frac{80,000}{(1+0.10)^2}$$ Calculate each term: $$\frac{60,000}{1.10} = 54,545.45$$ $$\frac{80,000}{1.10^2} = \frac{80,000}{1.21} = 66,115.70$$ Sum: $$-100,000 + 54,545.45 + 66,115.70 = 20,661.15$$ 5. **Calculate NPV if delay 1 year:** Initial outlay is delayed by 1 year, so it occurs at Year 1, discounted back to present: $$\text{NPV}_{delay} = -\frac{100,000}{(1+0.10)^1} + \frac{70,000}{(1+0.10)^2} + \frac{90,000}{(1+0.10)^3}$$ Calculate each term: $$-\frac{100,000}{1.10} = -90,909.09$$ $$\frac{70,000}{1.21} = 57,851.24$$ $$\frac{90,000}{1.331} = 67,591.44$$ Sum: $$-90,909.09 + 57,851.24 + 67,591.44 = 34,533.59$$ 6. **Decision:** Since $$\text{NPV}_{delay} = 34,533.59 > \text{NPV}_{now} = 20,661.15$$, Company F should delay investment by 1 year. **Final answer:** Delay investment by 1 year for higher NPV.