$4.$ What is the NPV of buying a new machine for $$100$m that will generate its first profit of $$10$m in year $5$ and continue generating the same amount of profit until year $10,$ after which the cash flow will grow at a $5\%$ rate per year? Assume the cost of capital is $10\%$

$5.$ You are evaluating Project A requiring an investment of $$100$m in year $0$ after which it will generate cash flows of $$50$m at the end of years $10$ to $20.$ The cost of capital is $8\%.$

a$.$ What is the project$$s NPV$?$

b$.$ What is its IRR?