Beta of dealership =2

Question is below but I do not understand beta formula used in soluo

I don't understand solution formula used in the beta. Please explain

modes cachondo Odramma 2020-10-3504301 beta Previous Next 22.3 The Option to Delay Investment a Call Option 831 TABLE 22.1 Black Scholes Option Value Parameters for Evaluating a Real Option to Invest Real Option Financial Option Stock Price Strike Price Expiration Date Risk-Free Rate Volatility of Stock Dividend S K 7 Example $6 million $5 million Current Market Value of Aset Upfront Investment Required Final Decision Date Risk-Free Rate Volatility of Aset Value FCF Lost from Delay 5% Dir 30.6 million Now we can compute the value of the call option to open the dealership using E4, 217 and Eq. 21.8. In(STPV, VT_In(5.46/4.70 0.200543 VT 2 0.40 d=-VT=0.543 -0.40 =0.143 and therefore, C=S'N) - PVN) (55.46 million) (0.706) -(841.76 million) (0557) = $1.20 million The female in 1 22.2 states that the value today from waiting time in the lake ship next year and on mingit if it profitable mode 51. The ced the NPV of $1 million from the celeship This wa what the advantage of the the likely of the file the When the value of the firm is $7 million turn it be optimal investiment. We can see the computing the value of the call similar to -1, -0,932,660.312, C5101 The value exercising immediately 057 - 55 - 53 million is greater than the value of the call (1 91 mm so the bea of the corporation is equal to the bea of the dealership: 2 22-10. Under the same asumptions in Section 12., uppose your corporation wwwperating electric car dealership, together with one year options to open fire mere What is the value and bets of your firm of the expected first year tree ashow for dealerships is $600.000 b. What is the value and beta of your firm if the expected first-year free how for all dealerships is $300.000 In which case de your options have higher betal in which cane does your firm love higher beta? Why? From section 22.3, the value of the operating dealership is 56 million and the value of a nyom call option is 1.2 million. Additionally from section 22.3. the beta of the operating dealership is 2. while the beta of the one your option is 64. The value of the firm is therefore (56551.2) - $12 million 56 5x512 x24 x64-42 P SL2 512 5. + b. For expected cash flows of $300,000, the value of the operating dealership is $3 million. The value of a one-year eallis 50.3 million SES-PY(Dev) = $3 million 52.73 million L12 4, In(2.73/476) +0.20-1190 dy=4-VT-0404-640 = 1.590 0.40 C-52.73x0.117-54.76x0.056 = 50.05 1.-(53+5.50.05) - $3.25 million. S**N(4) $2.73x0.117 x2-128 C $0.05 Badership 5xY + 53 5x50.05 x2+ x128=28 $3.25 The options have a higher beta when eash flows are lower (In part b). The firm has a higher bela when cash flows are higher (in part a). With higher cash flows, the beta of the option is lower because the option is closer to in-the-money. This causes the value of the option to be higher and to affect the value and beta of the firm. With higher cash flows, the beta of the firm will be higher firm with so the beta of the corporation is equal to the beta of the dealership: 2. 22-10. Under the same assumptions as in Section 22.3, suppose your corporation owns an opera electric car dealership, together with one-year options to open five more. a. What is the value and beta of your firm if the expected first-year free cash flow for dealerships is $600,000? b. What is the value and beta of your firm if the expected first-year free cash flow for dealerships is $300,000? In which case do your options have higher beta? In which case does your firm have highe beta? Why? a. From section 22.3. the value of the operating dealership is $6 million and the value of a one-year call option is $1.2 million. Additionally from section 22.3, the beta of the operating dealership is 2. while the beta of the one-year option is 6.4. The value of the firm is therefore Ve= ($6+5 * $1.2) = $12 million SxV $6 5x$1.2 -x21 x 6.4 -4.2 corporation V v $12 $12 c. gation b. For expected cash flows of $300,000, the value of the operating dealership is $3 million. The value of a one-year call is: SES PV(Div)$3 million 50.3 million $2,73 million 1.12 1.2.73/4.76) +0.20 1.190 dyd-VT -0404 0.40 1590 0.40 C-52.73x0.117-54.76x0.056 - 30.05 d Bcorporation Pealership V SV $6 5x$12 + -B -x2+ option Ex 6.4 -42 V. $12 $12 b. For expected cash flows of $300,000, the value of the operating dealership is $3 million. The value of a one-year call is: SES-PV(Dev)$3 million 30.3 million $2.73 million 1.12 In2.73/4.76) +0.20 = 1.190 dy=,-9/7 0404-0.40-1590 0.40 C-$2.73x0.117-$4.76x0.056 - $0.05 Ve= ($3+ 5 * $0.05) = $3.25 million. S'xN) Pedership Pcorporation Va dealership 1 $2.73x0.117 x2 = 12.8 $0.05 5xV $3 5x $0.05 Popien X21 x12828 corpor V V $3.25 $325 The options have a higher beta when cash flows are lower (in part b). The firm has a higher beta when cash flows are higher (in part a) With higher cash flows, the beta of the option is lower because the option is closer to in-the-money. This causes the value of the option to be higher and to affect the value and beta of the firm. With higher cash flows, the beta of the firm will be higher because a larger portion of its value comes from the value of the options. Intuitively, a firm with higher future expected cash flows in this setting has larger growth options, 22-11. The management of Southeru Express Corporation is considering investing 10% of all futur warning: in growth. The company has a single growth opportunity that it can take either non or