Capital Budgeting Practice

Full Answer Section

1. Calculate NPV for Initial Offer:

NPV=(1+0.10)01,000,000​+(1+0.10)1−500,000​+(1+0.10)2−500,000​+(1+0.10)3−500,000​NPV=1,000,000−1.10500,000​−1.21500,000​−1.331500,000​$$\text{NPV}=1,000,000-454,545.45-413,223.14-375,657.40$$$$\text{NPV}=-243,425.99$$

Decision: Since the NPV is negative $(-\$243,425.99)$, you should reject this initial offer.

2. Plot NPV vs. Discount Rate (Initial Offer):

To plot, we need NPV values at various discount rates (0% to 50%).

(Note: The NPV at 0% is calculated as $1,000,000-500,000-500,000-500,000=-500,000$. Subsequent NPVs are calculated similarly by changing the discount rate.)

3. Determine the IRR for Initial Offer:

The IRR is the discount rate at which NPV = 0. From the table above, we can see that the NPV turns positive somewhere between 20% and 25%. Using a financial calculator or software to find the exact IRR for the cash flows [1,000,000, -500,000, -500,000, -500,000]:IRR $\approx 22.95\%$

Scenario 2: New Offer ($550,000 Advance + $1,000,000 in Year 4)

Cash Flows:

• Year 0:
  • Advance: +$550,000
• Year 1:
  • Lost speaking engagements: -$500,000
• Year 2:
  • Lost speaking engagements: -$500,000
• Year 3:
  • Lost speaking engagements: -$500,000
• Year 4:
  • Book Payment: +$1,000,000

Opportunity Cost (Discount Rate): 10%

1. Calculate NPV for New Offer:

NPV=(1+0.10)0550,000​+(1+0.10)1−500,000​+(1+0.10)2−500,000​+(1+0.10)3−500,000​+(1+0.10)41,000,000​NPV=550,000−454,545.45−413,223.14−375,657.40+1.46411,000,000​$$\text{NPV}=550,000-454,545.45-413,223.14-375,657.40+682,904.17$$$$\text{NPV}=-110,521.82$$

Decision: Since the NPV is negative $(-\$110,521.82)$, you should reject this new offer.

2. Plot NPV vs. Discount Rate (New Offer):

(Note: NPV at 0% is $550,000-500,000-500,000-500,000+1,000,000=50,000$)

3. Determine the IRRs for New Offer:

The cash flows are: $[550,000,-500,000,-500,000,-500,000,1,000,000]$. Since there is a sign change in cash flows more than once (positive at Year 0, negative Years 1-3, positive Year 4), there is a possibility of multiple IRRs. This is characteristic of non-conventional cash flow streams.

Let's check the NPV profile for 0% and very high discount rates. At 0%, NPV = $50,000. At a very high discount rate, say 1000%, the positive cash flows at the beginning and end will be heavily discounted, and the intermediate negative cash flows will dominate relatively.

Using a financial calculator or software:

• IRR1 $\approx 3.73\%$
• IRR2 $\approx 141.68\%$

4. Discuss if the IRR rule for making budgetary decisions can be used in this case:

No, the IRR rule cannot be reliably used for making budgetary decisions in this specific case (Scenario 2 with the second offer).

Reasons:

• Multiple IRRs: The presence of multiple IRRs (3.73% and 141.68%) makes the IRR rule ambiguous. Which one should be compared to the cost of capital? Both? Neither? This ambiguity renders the decision rule ineffective. When cash flows alternate signs (a non-conventional cash flow stream), multiple IRRs can arise, leading to confusion about project acceptability.
• Reinvestment Rate Assumption: The IRR method inherently assumes that positive cash flows generated by the project are reinvested at the IRR itself. In this case, assuming reinvestment at 141.68% (or even 3.73%) is highly unrealistic. NPV, on the other hand, assumes reinvestment at the cost of capital, which is generally a more realistic and conservative assumption.
• Scale Problem (Not directly applicable here, but a general IRR issue): While not the primary issue here, IRR can also suffer from the scale problem where it might prefer a smaller project with a higher percentage return over a larger, more value-adding project with a lower percentage return.

In this case, the NPV method is superior and unambiguous. With an opportunity cost of 10%, the NPV of $-\$110,521.82$ clearly indicates that the project is not financially viable at that discount rate.

Scenario 3: New Offer ($750,000 Advance + $1,000,000 in Year 4)

Cash Flows:

• Year 0:
  • Advance: +$750,000
• Year 1:
  • Lost speaking engagements: -$500,000
• Year 2:
  • Lost speaking engagements: -$500,000
• Year 3:
  • Lost speaking engagements: -$500,000

Sample Answer

To solve this problem, we'll break it down into parts, calculating NPV and IRR for each scenario and then plotting the NPV profiles.

Scenario 1: Initial Offer

Cash Flows:

• Year 0:
  • Advance: +$1,000,000
  • Lost speaking engagements (Year 0 is typically when the project starts, so the first loss occurs at the end of Year 1, 2, 3): $0
• Year 1:
  • Lost speaking engagements: -$500,000
• Year 2:
  • Lost speaking engagements: -$500,000
• Year 3:
  • Lost speaking engagements: -$500,000
• Year 4 and beyond: $0 (Book is assumed to be published, writing stops)

Opportunity Cost (Discount Rate): 10%