Give step-by-step solution with explanation and final answer:

You are an investment bank intern and your first job is to help with an acquisition project. Your client, Purifier, is an industry leade

Question

Give step-by-step solution with explanation and final answer:

You are an investment bank intern and your first job is to help with an acquisition project. Your client, Purifier, is an industry leader in the air conditioning business. Recently, Purifier approached your investment bank and expressed its interests in acquiring a start
-
up called IntelAir. Your project manager assigned you the task of evaluating this acquisition. After one week of research, you gathered the following information about IntelAir.IntelAir was founded two years ago by a few college dropouts. IntelAir has developed a proprietary temperature sensor antenna and a patented air purifying system. Purifier thinks that acquiring IntelAir will bring valuable economic synergies and expand Purifier
’
s market share.IntelAir has signed contracts with several temperature sensor companies to deliver its antenna. The contract specifies that over the next ten years 
(
years 
1
 ﻿to 
1
0
)
,
 ﻿IntelAir would deliver their most up
-
to
-
date sensor antennas for $
1
0
0
0
/
unit
.
 ﻿The yearly order volume is 
5
0
0
0
 ﻿units for a total revenue of $
5
,
0
0
0
,
0
0
0
.
 ﻿After 
1
0
 ﻿years, IntelAir anticipates that the

VIPSolutions · Accepted Answer

Let's break the problem into steps and solve for the **maximum price Purifier should pay for IntelAir** using **Discounted Cash Flow (DCF)** analysis.

---

## **Step 1: Revenue Calculation**

- **Annual revenue (Years 1-10):**
  - Price per unit = \$1000
  - Units per year = 5000
  - **Annual revenue = 5000 × \$1000 = \$5,000,000**

- **Total years of revenue = 10 (Years 1 to 10)**

---

## **Step 2: Production Cost Calculation**

- **Annual production cost:**
  - Cost per unit = \$700
  - Units per year = 5000
  - **Annual cost = 5000 × \$700 = \$3,500,000**

- **Special cost in Year 5:** Technology upgrade = \$800,000

---

## **Step 3: Patent Sale**

- **In Year 1**, Purifier plans to sell the patent for **\$2,000,000.**

---

## **Step 4: Calculate Annual Cash Flows (Years 1-10)**

- **Annual cash flow (Years 1-10):**
  - Revenue - Cost = \$5,000,000 - \$3,500,000 = **\$1,500,000** per year

- **Year 5:** Subtract upgrade expense:
  - Cash flow = \$1,500,000 - \$800,000 = **\$700,000**

- **Year 1:** Add patent sale:
  - Cash flow = \$1,500,000 + \$2,000,000 = **\$3,500,000**

---

## **Step 5: List Cash Flows per Year**

| Year | Cash Flow |
|------|-----------|
| 1    | \$3,500,000 |
| 2    | \$1,500,000 |
| 3    | \$1,500,000 |
| 4    | \$1,500,000 |
| 5    | \$700,000   |
| 6    | \$1,500,000 |
| 7    | \$1,500,000 |
| 8    | \$1,500,000 |
| 9    | \$1,500,000 |
| 10   | \$1,500,000 |

---

## **Step 6: Discount the Cash Flows**

Using discount rate $ r = 10\% $, present value of cash flow in year $ n $:

$$
PV = \frac{CF}{(1 + r)^n}
$$

Let's calculate each year's present value:

#### **Year 1:**
$$
PV_1 = \frac{3,500,000}{1.10^1} = \frac{3,500,000}{1.10} = 3,181,818.18
$$

#### **Year 2:**
$$
PV_2 = \frac{1,500,000}{1.10^2} = \frac{1,500,000}{1.21} = 1,239,669.42
$$

#### **Year 3:**
$$
PV_3 = \frac{1,500,000}{1.10^3} = \frac{1,500,000}{1.331} = 1,127,987.34
$$

#### **Year 4:**
$$
PV_4 = \frac{1,500,000}{1.10^4} = \frac{1,500,000}{1.4641} = 1,024,352.62
$$

#### **Year 5:**
$$
PV_5 = \frac{700,000}{1.10^5} = \frac{700,000}{1.61051} = 434,567.31
$$

#### **Year 6:**
$$
PV_6 = \frac{1,500,000}{1.10^6} = \frac{1,500,000}{1.771561} = 847,086.88
$$

#### **Year 7:**
$$
PV_7 = \frac{1,500,000}{1.10^7} = \frac{1,500,000}{1.9487171} = 769,635.34
$$

#### **Year 8:**
$$
PV_8 = \frac{1,500,000}{1.10^8} = \frac{1,500,000}{2.14358881} = 699,292.52
$$

#### **Year 9:**
$$
PV_9 = \frac{1,500,000}{1.10^9} = \frac{1,500,000}{2.357947691} = 636,629.57
$$

#### **Year 10:**
$$
PV_{10} = \frac{1,500,000}{1.10^{10}} = \frac{1,500,000}{2.5937424601} = 578,392.94
$$

---

## **Step 7: Add up the Present Values**

Sum all the present values:

$$
\begin{align*}
PV_{total} = & 3,181,818.18 \
            & + 1,239,669.42 \
            & + 1,127,987.34 \
            & + 1,024,352.62 \
            & +   434,567.31 \
            & +   847,086.88 \
            & +   769,635.34 \
            & +   699,292.52 \
            & +   636,629.57 \
            & +   578,392.94 \
\end{align*}
$$

Let's add them up:

- $ 3,181,818.18 + 1,239,669.42 = 4,421,487.60 $
- $ + 1,127,987.34 = 5,549,474.94 $
- $ + 1,024,352.62 = 6,573,827.56 $
- $ + 434,567.31 = 7,008,394.87 $
- $ + 847,086.88 = 7,855,481.75 $
- $ + 769,635.34 = 8,625,117.09 $
- $ + 699,292.52 = 9,324,409.61 $
- $ + 636,629.57 = 9,961,039.18 $
- $ + 578,392.94 = 10,539,432.12 $

---

## **Final Answer**

**The maximum Purifier should pay for IntelAir is:**

$$
\boxed{\$10,539,432.12}
$$

*(rounded to two decimal digits, as requested)*

---

### **Summary Table**

| Year | Cash Flow | Discount Factor | Present Value      |
|------|-----------|----------------|--------------------|
| 1    | 3,500,000 | 0.9091         | 3,181,818.18       |
| 2    | 1,500,000 | 0.8264         | 1,239,669.42       |
| 3    | 1,500,000 | 0.7513         | 1,127,987.34       |
| 4    | 1,500,000 | 0.6830         | 1,024,352.62       |
| 5    |   700,000 | 0.6209         |   434,567.31       |
| 6    | 1,500,000 | 0.5645         |   847,086.88       |
| 7    | 1,500,000 | 0.5132         |   769,635.34       |
| 8    | 1,500,000 | 0.4665         |   699,292.52       |
| 9    | 1,500,000 | 0.4241         |   636,629.57       |
| 10   | 1,500,000 | 0.3855         |   578,392.94       |
| **Sum** |           |                | **\$10,539,432.12** |

---

### **Conclusion**

**Purifier should pay at most \$10,539,432.12 for IntelAir.**

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