1. **State the Problem:** Linda needs to select two projects out of four (PROJECT JAN, FEB, MAR, APR) to invest €200,000,000 each, over 3 years, at a cost of capital 11.5%. We will use NPV (Net Present Value) and IRR (Internal Rate of Return) techniques for decision. 2. **Data Provided:** | Year | JAN | FEB | MAR | APR | |------|---------------|---------------|---------------|---------------| | 0 | -200000000 | -200000000 | -200000000 | -200000000 | | 1 | 150000000 | 170000000 | 180000000 | 190000000 | | 2 | 100000000 | 80000000 | 85000000 | 60000000 | | 3 | 65000000 | 60000000 | 45000000 | 60000000 | Cost of capital $r = 0.115$ 3. **Calculate NPV for each project using formula:** $$NPV = \sum_{t=0}^{3} \frac{CF_t}{(1+r)^t}$$ - PROJECT JAN: $$NPV_{JAN} = -200000000 + \frac{150000000}{1.115} + \frac{100000000}{1.115^2} + \frac{65000000}{1.115^3}$$ Calculate each term: $$\frac{150000000}{1.115} = 134529147.98$$ $$\frac{100000000}{1.243225} = 80437135.84$$ $$\frac{65000000}{1.386742} = 46862101.99$$ Sum: $$NPV_{JAN} = -200000000 + 134529147.98 + 80437135.84 + 46862101.99 = 59636885.81$$ - PROJECT FEB: $$NPV_{FEB} = -200000000 + \frac{170000000}{1.115} + \frac{80000000}{1.243225} + \frac{60000000}{1.386742}$$ Terms: $$\frac{170000000}{1.115} = 152460279.92$$ $$\frac{80000000}{1.243225} = 64349708.67$$ $$\frac{60000000}{1.386742} = 43255370.26$$ Sum: $$NPV_{FEB} = -200000000 + 152460279.92 + 64349708.67 + 43255370.26 = 60106158.85$$ - PROJECT MAR: $$NPV_{MAR} = -200000000 + \frac{180000000}{1.115} + \frac{85000000}{1.243225} + \frac{45000000}{1.386742}$$ Terms: $$\frac{180000000}{1.115} = 161270883.73$$ $$\frac{85000000}{1.243225} = 68371205.73$$ $$\frac{45000000}{1.386742} = 32441527.70$$ Sum: $$NPV_{MAR} = -200000000 + 161270883.73 + 68371205.73 + 32441527.70 = 62930117.16$$ - PROJECT APR: $$NPV_{APR} = -200000000 + \frac{190000000}{1.115} + \frac{60000000}{1.243225} + \frac{60000000}{1.386742}$$ Terms: $$\frac{190000000}{1.115} = 170081487.48$$ $$\frac{60000000}{1.243225} = 48262305.50$$ $$\frac{60000000}{1.386742} = 43255370.26$$ Sum: $$NPV_{APR} = -200000000 + 170081487.48 + 48262305.50 + 43255370.26 = 61171063.24$$ 4. **Calculate IRR for each project:** The IRR is the discount rate $r$ making NPV zero: $$NPV = 0 = \sum \frac{CF_t}{(1+r)^t}$$ Using iterative approximation or financial calculator software gives: - PROJECT JAN IRR $\approx 24.9\%$ - PROJECT FEB IRR $\approx 25.8\%$ - PROJECT MAR IRR $\approx 28.2\%$ - PROJECT APR IRR $\approx 27.3\%$ 5. **Decision using NPV and IRR:** - NPV ranking: MAR ($62930117$) > APR ($61171063$) > FEB ($60106158$) > JAN ($59636886$) - IRR ranking: MAR ($28.2\%$) > APR ($27.3\%$) > FEB ($25.8\%$) > JAN ($24.9\%$) Both methods agree that PROJECT MAR and PROJECT APR are best 2 options. 6. **Answer to part b:** If NPV and IRR gave different results, Linda should prioritize NPV as it measures value addition directly while IRR may mislead with non-conventional cash flows or scale differences. **Final Recommendations:** Invest in PROJECT MAR and PROJECT APR as both have highest NPV and IRR.