Hi Darren!
Great question! This is a corporate valuation problem involving mergers, acquisition costs, risk, and growth rates.
The main idea is that an acquisition should increase the total value of the acquiring company's shareholders' investment.
Let's solve each part step by step.
Step 1: Identify the information
We are given:
| VariableValue | |
| Acquisition price | $980,000 |
| Gojeck's first-year net income | $195,000 |
| Annual depreciation | $5,000 |
| Existing annual net cash flow | $900,000 |
| Original growth rate | 6% |
| Original required return | 14% |
| Required return after acquisition | 15% |
| Growth rate in Part III | 8% |
For this problem, we'll assume depreciation is the only adjustment needed to convert Gojeck's net income into cash flow, and that the stated cash flows are available to the capital providers.
Step 2: Calculate Gojeck's annual cash flow
We are told that Gojeck is expected to generate $195,000 in net income during its first year.
Since depreciation is a noncash expense, we add it back:
[
CF_1=NI+\text{Depreciation}
]
[
CF_1=195,000+5,000
]
[
\boxed{CF_1=$200,000}
]
Therefore, Gojeck's first-year cash flow is estimated at $200,000.
For the valuation below, we'll assume this cash flow grows at 6% annually.
Part I: Should Grabs Acquire Gojeck?
Step 1: Calculate Grabs' value without the acquisition
We use the growing perpetuity formula:
[
V=\frac{CF_1}{r-g}
]
Where:
- (CF_1) = Cash flow expected next year
- (r) = Required rate of return
- (g) = Constant growth rate
Grabs currently generates $900,000 in cash flow, which is expected to grow at 6%.
Therefore, next year's cash flow is:
[
CF_1=900,000(1.06)
]
[
CF_1=$954,000
]
Using the original required return of 14%:
[
V_{\text{without}}=\frac{954,000}{0.14-0.06}
]
[
V_{\text{without}}=\frac{954,000}{0.08}
]
[
\boxed{V_{\text{without}}=$11,925,000}
]
This represents Grabs' estimated value if it does not acquire Gojeck.
Step 2: Calculate Grabs' value after the acquisition
The acquisition increases the required return to 15%.
First, calculate the value of Grabs' existing operations using the higher discount rate:
[
V_{\text{existing}}=\frac{954,000}{0.15-0.06}
]
[
V_{\text{existing}}=\frac{954,000}{0.09}
]
[
\boxed{V_{\text{existing}}=$10,600,000}
]
Now calculate Gojeck's value:
[
V_{\text{Gojeck}}=\frac{200,000}{0.15-0.06}
]
[
V_{\text{Gojeck}}=\frac{200,000}{0.09}
]
[
\boxed{V_{\text{Gojeck}}=$2,222,222.22}
]
The combined company's value before paying the acquisition price is:
[
V_{\text{combined}}=10,600,000+2,222,222.22
]
[
\boxed{V_{\text{combined}}=$12,822,222.22}
]
Step 3: Subtract the acquisition price
Grabs must pay $980,000 to acquire Gojeck.
Therefore:
[
V_{\text{after}}=12,822,222.22-980,000
]
[
\boxed{V_{\text{after}}=$11,842,222.22}
]
Step 4: Compare the two values
Without the acquisition:
[
V_{\text{without}}=$11,925,000
]
After the acquisition:
[
V_{\text{after}}=$11,842,222.22
]
The difference is:
[
\Delta V=11,842,222.22-11,925,000
]
[
\boxed{\Delta V=-$82,777.78}
]
Answer to Part I: NO.
Grabs should not acquire Gojeck under these assumptions because the acquisition would reduce shareholder value by approximately $82,778.
Although Gojeck generates positive cash flows, the increased required return reduces the value of Grabs' existing operations enough to offset the acquisition's benefits.
Part II: What If the Required Rate of Return Remains at 14%?
Now assume the acquisition does not increase Grabs' required return.
The required return remains 14%.
Step 1: Value Grabs' existing operations
We already calculated:
[
V_{\text{existing}}=$11,925,000
]
Step 2: Value Gojeck using the 14% discount rate
[
V_{\text{Gojeck}}=\frac{200,000}{0.14-0.06}
]
[
V_{\text{Gojeck}}=\frac{200,000}{0.08}
]
[
\boxed{V_{\text{Gojeck}}=$2,500,000}
]
Step 3: Calculate the combined value after acquisition costs
[
V_{\text{after}}=11,925,000+2,500,000-980,000
]
[
\boxed{V_{\text{after}}=$13,445,000}
]
Step 4: Calculate the increase in shareholder value
[
\Delta V=13,445,000-11,925,000
]
[
\boxed{\Delta V=$1,520,000}
]
Answer to Part II: YES.
If the required return remains at 14%, Grabs should acquire Gojeck.
The acquisition would increase shareholder value by approximately $1.52 million.
This illustrates an important financial principle:
A lower required rate of return increases the present value of future cash flows.
Part III: What If the Acquisition Increases the Company's Growth Rate to 8% Forever?
Now suppose the acquisition raises the surviving company's perpetual growth rate from 6% to 8%.
We'll assume the required return still increases to 15%.
We'll also assume the new 8% growth rate applies to the combined company's current cash-flow base of $1,100,000.
Step 1: Calculate the combined cash-flow base
[
CF_0=900,000+200,000
]
[
\boxed{CF_0=$1,100,000}
]
Step 2: Calculate next year's cash flow
With an 8% growth rate:
[
CF_1=1,100,000(1.08)
]
[
\boxed{CF_1=$1,188,000}
]
Step 3: Calculate the combined company's value
Using the growing perpetuity formula:
[
V_{\text{combined}}=\frac{1,188,000}{0.15-0.08}
]
[
V_{\text{combined}}=\frac{1,188,000}{0.07}
]
[
\boxed{V_{\text{combined}}=$16,971,428.57}
]
Step 4: Subtract the acquisition price
[
V_{\text{after}}=16,971,428.57-980,000
]
[
\boxed{V_{\text{after}}=$15,991,428.57}
]
Step 5: Compare with Grabs' original value
[
\Delta V=15,991,428.57-11,925,000
]
[
\boxed{\Delta V=$4,066,428.57}
]
Answer to Part III: YES.
If the acquisition permanently increases the combined company's growth rate to 8%, Grabs should acquire Gojeck.
Under our assumptions, the acquisition increases shareholder value by approximately $4.07 million.
The higher growth rate more than compensates for the increase in the required return.
Final Answers
| ScenarioChange in Shareholder ValueAcquire Gojeck? | ||
| I. Required return rises to 15%; growth remains 6% | −$82,777.78 | No |
| II. Required return stays at 14%; growth remains 6% | +$1,520,000 | Yes |
| III. Required return rises to 15%; growth increases to 8% | +$4,066,428.57 | Yes |
What Should We Learn From This Problem?
There are three important takeaways.
1. Acquisitions should create shareholder value.
A company should not acquire another business simply because that business is profitable. The acquisition must create enough value to justify its purchase price.
2. Risk affects valuation.
When the required return increases, the present value of future cash flows decreases.
3. Growth can create substantial value.
A permanent increase in expected cash-flow growth can significantly increase a company's valuation, provided the growth rate remains below the required return.
One important assumption: Part III does not explicitly state whether Gojeck's $200,000 first-year cash flow should be treated as part of the current cash-flow base or as a separate first-year payment. The calculation above treats it as part of the base. A different timing convention would produce a somewhat different numerical answer, although the acquisition decision would remain favorable.
Hope this helps!
Michael
