Problem 1.A startup company called "LumiereBeauty" is being evaluated by its founders at datet= 0, which is the beginning of itsgrowth period. The growth period is ex- pected to last for 5 years. After the growth period, LumiereBeauty will enter into theearly-maturity period. The early-maturity period is expected to last for 15 years. After it finishes the early-maturity period, the founders of LumiereBeauty expect the company to enter thelate-maturity period. The late-maturity period is expected to last forever.

In the growth period, the growth rate of invested capital is 100%, the return on invested capital is 15%, and the required rate of return is 20%. In the early-maturity period, the growth rate is 10%, the return on invested capital is 50%, and the required rate of return is 12%. In the late-maturity period, the growth rate decreases to 3%, the return on invested capital is 8% and is equal to the required rate of return. The amount of invested capital in LumiereBeauty at the beginning of the growth period is $3 million.

1. What is the economic value att= 0 of the free cash flows LumiereBeauty is expected to produce during the growth period?

2. What is the economic value att= 0 of the free cash flows LumiereBeauty is expected to produce during the early-maturity period?

3. What is the economic value att= 0 of the free cash flows LumiereBeauty is expected to produce during the late-maturity period?

4. What is the economic value of LumiereBeauty att= 0?

5. If the growth rate in the late-maturity period is 15%, compute by how much the economic

value of LumiereBeauty att= 0 changes. Explain the result using one or two sentences.

6. If the return on invested capital in the early-maturity period increases to 75%, does the value of LumiereBeauty att= 0 change? If it changes, compute the new value and explain why the value changes. If it does not change, please explain why the value does not change.