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Homework answers / question archive / Rearden Metal can invest in a risk-free technology that requires an up-front investment of $1 million

Rearden Metal can invest in a risk-free technology that requires an up-front investment of $1 million. Rearden's managers are hesitant to invest because of uncertainty over future interest rates. Suppose that all interest rates will be either 8% or 4% in one year and remain there forever. The risk-neutral probability that interest rates will drop to 4% is 40%. The one-year risk-free interest rate is 5% and today's rate on a risk-free perpetual bond is 6%. The rate on an equivalent perpetual bond that is repayable at any time (the callable annuity rate) is 7.65%.

1) Assuming that this project will provide Rearden with perpetual annual cash flows of $55,000, the NPV of investing in the project today is closest to:

A) -281,000

B) -150,000

C) -83,000

D) +83,000

E) +281,000

2) Assuming that this project will provide Rearden with perpetual annual cash flows of $55,000, the NPV of investing in the project next year is closest to:

A) -281,000

B) -83,000

C) +46,000

D) +83,000

E) +143,000

3) Assuming that this project will provide Rearden with perpetual annual cash flows of $55,000, the NPV of investing in the project today using the hurdle rate is closest to:

A) -281,000

B) -150,000

C) -83,000

D) +83,000

E) +281,000

4) Assuming that this project will provide Rearden with perpetual annual cash flows of $45,000, Rearden should:

A) invest today since the NPV is positive.

B) invest today since the NPV is negative.

C) invest today since the NPV using the hurdle rate is negative.

D) delay investing since the NPV using the hurdle rate is negative.

E) delay investing since the NPV using the hurdle rate is positive.

5) Assuming that this project will provide Rearden with perpetual annual cash flows of $65,000, the NPV of investing in the project today is closest to:

A) -281,000

B) -83,000

C) +46,000

D) +83,000

E) +143,000

6) Assuming that this project will provide Rearden with perpetual annual cash flows of $65,000, the NPV of investing in the project next year is closest to:

A) -281,000

B) +46,000

C) +83,000

D) +143,000

E) +238,000

7) Assuming that this project will provide Rearden with perpetual annual cash flows of $65,000, the NPV of investing in the project today using the hurdle rate is closest to:

A) -281,000

B) -150,000

C) -83,000

D) +83,000

E) +281,000

8) Assuming that this project will provide Rearden with perpetual annual cash flows of $65,000, Rearden should:

A) invest today since the NPV is positive.

B) invest today since the NPV is negative.

C) invest today since the NPV using the hurdle rate is positive.

D) delay investing since the NPV using the hurdle rate is negative.

E) delay investing since the NPV using the hurdle rate is positive.

9) Assuming that this project will provide Rearden with perpetual annual cash flows of $80,000, the NPV of investing in the project today using the hurdle rate is closest to:

A) -281,000

B) +46,000

C) +83,000

D) +143,000

E) +238,000

10) Assuming that this project will provide Rearden with perpetual annual cash flows of $80,000, Rearden should:

A) invest today since the NPV is positive.

B) invest today since the NPV is negative.

C) invest today since the NPV using the hurdle rate is positive.

D) delay investing since the NPV using the hurdle rate is negative.

E) delay investing since the NPV using the hurdle rate is positive.

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